diff options
Diffstat (limited to 'Master')
29 files changed, 0 insertions, 14322 deletions
diff --git a/Master/texmf-dist/doc/amstex/siam/amsamp.tex b/Master/texmf-dist/doc/amstex/siam/amsamp.tex deleted file mode 100644 index 44048937dd7..00000000000 --- a/Master/texmf-dist/doc/amstex/siam/amsamp.tex +++ /dev/null @@ -1,365 +0,0 @@ -% This is the sample paper for the AmSTeX SIAM style file, (amstex)siam.sty -% for use with AmSTeX version 2.1 or later and amsppt.sty, version 2.1a. -% RCS information: $Revision: 1.1 $, $Date: 93/01/25 15:33:19 $. -\input amstex -\documentstyle{amstexs1} -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% Macro definitions for running heads and first page % -\accepted\SIMAF % -\firstpageno{10} % -\lastpageno{12} % -\issuevolume{1} % -\issuenumber{2} % -\issuemonth{February} % -\placenumber{002} % place of paper in this issue % -\issueyear{1988} % -\shortauthor{Bradley J. Lucier and Douglas N. Arnold} % -\shorttitle{A Sample Paper} % -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% Macros specific to this paper % -\define\loner{{L^1(\Bbb R)}} % -\define\linfr{{L^\infty(\Bbb R)}} % -\define\bvr{{\roman{BV}(\Bbb R)}} % -\define\TV{{\roman {TV}}} % -\define\sdot{\,\cdot\,} % -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\topmatter -\title -A SAMPLE PAPER, WITH A RATHER LONG TITLE, TO ILLUSTRATE THE -\AmSTeX\ SIAM STYLE\footnote[\boldkey*]{Unlikely to appear.} -\endtitle -\author -BRADLEY J. LUCIER\footnote[\dag]{Department of Mathematics, Purdue University, -West Lafayette, Indiana 47907. Present address, somewhere on the beach -(lucier\@math.purdue.edu). -The work of the first author was not supported by the -Wolf Foundation.}\ and DOUGLAS N. ARNOLD\footnote[\ddag]{Department -of Mathematics, Pennsylvania State University, -University Park, Pennsylvania 16802.} -\endauthor -\abstract -This sample paper illustrates many of the amstex -macros as used with the \AmSTeX\ SIAM style file amstexsiam (version 2.0a). -The \AmSTeX\ SIAM style file, which -inputs and builds upon the amsppt style (version 2.1a or later) -of Michael Spivak, gives authors easy -access to most of the typographical constructions used in SIAM journals. -It does not address the issues of the table of contents -or tables, which must be set using more primitive \TeX\ macros. -\endabstract -\keywords -porous medium, interface curves -\endkeywords -\subjclass -65N60 -\endsubjclass -\endtopmatter -\document -\subhead 1. Introduction\endsubhead -We are concerned with numerical approximations to the so-called -porous-medium equation \cite{6}, -$$ -\alignedat2 - &u_t=\phi(u)_{xx},&&\qquad x\in\Bbb R,\quad t>0,\quad\phi(u)=u^m,\quad m>1, -\\ - &u(x,0)=u_0(x),&&\qquad x\in\Bbb R. -\endalignedat -\tag 1.1 -$$ -We assume that the initial data $u_0(x)$ has bounded support, that -$0\leq u_0\leq M$, and that $\phi(u_0)_x\in\bvr$. -It is well known that a unique solution $u(x,t)$ of (1.1) exists, -and that $u$ satisfies -$$ - 0\leq u\leq M\text{ and }\TV\phi(u(\,\cdot\,,t))_x\leq\TV\phi(u_0)_x. -\tag 1.2 -$$ -If the data has slightly more regularity, then this too is satisfied -by the solution. Specifically, if $m$ is no greater than two and -$u_0$ is Lipschitz continuous, then $u(\,\cdot\,,t)$ is also Lipschitz; -if $m$ is greater than two and $(u_0^{m-1})_x\in\linfr$, then -$(u(\,\cdot\,,t)^{m-1})_x\in\linfr$ -(see [3]). (This will follow from results presented here, also.) -We also use the fact that the solution $u$ is H\"older continuous in $t$. - -\subhead 2. $\linfr$ error bounds\endsubhead -After a simple definition, we state a theorem -that expresses the error of approximations $u^h$ in -terms of the weak truncation error $E$. -\definition{Definition 2.1}\rm A {\it definition} -is the same as a theorem set in roman -type. In version 2 of the \AmSTeX\ style file for the SIAM journals, -definitions are set with their own command. -\enddefinition -\proclaim{Theorem 2.1} -Let $\{u^h\}$ be a family of approximate solutions satisfying -the following conditions for $0\leq t\leq T${\rm:} -\roster -\item For all $x\in\Bbb R$ and positive $t$, $0\leq u^h(x,t)\leq M${\rm;} -\item Both $u$ and $u^h$ are H\"older--$\alpha$ in $x$ -for some $\alpha\in(0,1\wedge 1/(m-1))${\rm;} $u^h$ is right -continuous in $t${\rm;} -and $u^h$ is H\"older continuous in $t$ on -strips $\Bbb R\times(t^n,t^{n+1})$, with the set $\{t^n\}$ having no -limit points\/{\rm;} and -\item There exists a positive function $\omega(h,\epsilon)$ such that\/{\rm:} -whenever $\{w^\epsilon\}_{0<\epsilon\leq\epsilon_0}$ is a family of functions -in $\bold X$ for which -{\roster -\item"(a)" there is a sequence of positive numbers $\epsilon$ tending -to zero, such that for these values of -$\epsilon$, $\|w^\epsilon\|_\infty\leq 1/\epsilon$, -\item"(b)" for all positive -$\epsilon$, $\|w_x^\epsilon(\sdot,t)\|_\loner\leq 1/\epsilon^2$, and -\item"(c)" for all $\epsilon>0$, -$$ -\sup\Sb -x\in\Bbb R\\0\leq t_1,t_2\leq T\endSb -\dfrac{|w^\epsilon(x,t_2)-w^\epsilon(x,t_1)|}{|t_2-t_1|^p}\leq 1/\epsilon^2, -$$ -where $p$ is some number not exceeding $1$, -\endroster}% -then\footnote{This is an obvious ploy, but we need a footnote.} - $|E (u^h,w^\epsilon,T)|\leq\omega(h,\epsilon).$ -\item -This is the fourth item in the outer roster. -\endroster -Then, there is a constant $C=C(m,M,T)$ such that -$$\multline -\|u-u^h\|_{\infty,\Bbb R\times[0,T]}\leq C\biggl[ -\sup \biggl |\int_\Bbb R(u_0(x)-u^h(x,0)) w(x,0) \,dx\biggr|\\ -+\omega(h,\epsilon)+\epsilon^\alpha\biggr],\endmultline -\tag 2.1 -$$ -where the supremum is taken over all $w\in\bold X$. -\endproclaim - -\demo{Proof} -We assume first that $Q$ is decreasing and consider the following cases: -\case{Case\/ {\rm1:} -$b'\geq 1/2$} We have $P(1/8)\geq\delta>0$ where $\delta$ -depends only on $d$, for otherwise by (3.7) applied to $P$ and $p=\infty$, -$P$ could not attain the value $1$ at $x=1$. Similarly, for -$m=(a'+b')/2$, $Q(m)\geq\delta'>0$ for some $\delta'$ depending only on $d$ -since otherwise $Q$ cannot attain the value $1$ at $x=a'$. Hence, for -$\delta''=\min(\delta,\delta')$, -$|A(y)|\geq|m-1/8|\geq b'/4\geq\frac18\max(b',1)$ for -$y\in[0,\delta'']$. On the other hand, -$|A(y)|\leq \max(b',1)$ for all $y\in[0,1]$, so (4.2) follows for -all $1\leq p\leq\infty$. -\endcase -\case{Case\/ {\rm2:} -$b'\leq 1/2$} We have $P(3/4)\leq\delta<1$ with $\delta$ -depending only on $d$ for otherwise (3.7) applied to $1-P$ and $p=\infty$ -would show that $P$ could not attain the value $0$ at $x=0$. It follows -that $|A(y)|\geq 3/4-b'\geq 1/4$, $y\in[\delta,1]$, while $|A(y)|\leq 1$ -for all $y\in[0,1]$. Hence (4.2) follows for -all $1\leq p\leq\infty$. -\endcase -We consider now when $Q$ is increasing. We can assume that $Q$ is not -a translate of $P$, i.e\., we do not have $P(x)=Q(x+\delta)$ for some $\delta$, -for then (4.2) follows trivially. In what follows, $C$ and $\delta$ -depend on $d$, and $C$ may depend on $p$. We consider the following cases: -\case{Case\/ {\rm3:} $a'\geq 1/4$ and $b'\leq 100$} -From (3.7) for $P$ -and $p=\infty$, it follows that $P(1/8)\geq\delta$ since otherwise $P$ cannot -attain the value $1$ at $x=1$. Hence $|A(y)|\geq a'-1/8\geq1/8$ on -$[0,\delta]$. On the other hand $|A(y)|\leq b'$ for all $y\in[0,1]$ and hence -(4.2) follows for all $1\leq p\leq\infty$. -\endcase -Let $z$ be in $\bold X$. Because $E(u,\sdot,\sdot)\equiv0$, -Equation (1.5) implies that -$$ -\int_\Bbb R\Delta uz|^T_0dx=\int_0^T\int_\Bbb R -\Delta u(z_t+\phi[u,u^h]z_{xx})\,dx\,dt- -E(u^h,z,t), -\tag 2.2 -$$ -where $\Delta u=u-u^h$ and -$$ -\phi[u,u^h]=\dfrac{\phi(u)-\phi(u^h)}{u-u^h}. -$$ -Extend $\phi[u,u^h](\cdot,t)=\phi[u,u^h](\cdot,0)$ for negative $t$, and -$\phi[u,u^h](\cdot,t)=\phi[u,u^h](\cdot,T)$ -for $t>T$. -Fix a point $x_0$ and a number $\epsilon>0$. Let $j_\epsilon$ -be a smooth function of $x$ with integral $1$ and support in -$[-\epsilon,\epsilon]$, -and let $J_\delta$ be a smooth function of -$x$ and $t$ with integral $1$ and support in -$[-\delta,\delta]\times[-\delta,\delta]$; $\delta$ and $\epsilon$ are -positive numbers to be specified later. -We choose $z=z^{\epsilon\delta}$ to satisfy -$$ -\aligned - &z_t+(\delta+J_\delta*\phi[u,u^h])z_{xx}=0,\qquad x\in\Bbb R,\;0 -\leq t\leq T,\\ - &z(x,T)=j_\epsilon(x-x_0). -\endaligned -\tag 2.3 -$$ -The conclusion of the theorem now follows from (2.1) and the fact that -$$ -|j_\epsilon*\Delta u(x_0,t)-\Delta u(x_0,t)|\leq C\epsilon^\alpha, -$$ -which follows from Assumption 2. -\qquad\qed -\enddemo -\example{Example\/ {\rm 1}} This is an example of an example. -\endexample -\remark{Remark\/ {\rm 1}} Examples are set the same as definitions in -some styles, -and the same as proofs in others. What convention does this style follow? -\endremark -Sometimes you want to include a figure, as in Fig.~1. -\topinsert -\def\Bif{{\bf if\/ }}\def\Bwhile{{\bf while\/ }}\def\Belse{{\bf else\/ }} -\settabs\+\qquad&\qquad&\qquad&\qquad&\cr -\+\smc Tree Partition Algorithm \{\cr -\+&Let stack size denote the number of nodes in the\cr -\+&&subtrees stored temporarily on the local stack\cr -\+&pop I from global stack\cr -\+&set stack size := 0\cr -\+&\Bwhile (stack size $\leq$ max size and stack size + -I$\rightarrow$tree size $>$ 3 (max size)) \{\cr -\+&&process I as an interior node\cr -\+&&let min tree be the smaller of the subtrees of the two children of I\cr -\+&&let max tree be the larger of the subtrees of the two children of I\cr -\+&&\Bif (min tree$\rightarrow$tree size + stack size $>$ 3 (max size)) \{\cr -\+&&&push min tree onto the global stack\cr -\+&&\} \Belse \{\cr -\+&&&push min tree onto the local stack\cr -\+&&&set stack size := stack size + min tree$\rightarrow$tree size\cr -\+&&\}\cr -\+&&set I := max tree\cr -\+&\}\cr -\+&\Bif (I$\rightarrow$tree size + stack size $>$ 3 (max size)) \{\cr -\+&&push I onto the global stack\cr -\+&\} \Belse \{\cr -\+&&push I onto the local stack\cr -\+&\}\cr -\+&Process all subtrees on the local stack\cr -\+\}\cr -\botcaption{Fig.~1} Tree partition algorithm Tree partition algorithm -Tree partition algorithm Tree partition algorithm Tree partition algorithm -Tree partition algorithm Tree partition algorithm.\endcaption -\endinsert - -We finish with a table of all SIAM journals. -\midinsert -\topcaption{Table 1}{SIAM journal acronyms and titles}\endcaption -\settabs\+\indent&Acronym\indent&Title&\cr -\hbox to \hsize{\hrulefill} -\+&Acronym&Title&\cr -\hbox to \hsize{\hrulefill} -\+&SINUM&SIAM Journal on Numerical Analysis&\cr -\+&SIREV&SIAM Review&\cr -\+&SIMA&SIAM Journal on Mathematical Analysis&\cr -\+&SIMAX&SIAM Journal on Matrix Analysis and Applications&\cr -\+&SICOMP&SIAM Journal on Computing&\cr -\+&SISC&SIAM Journal on Scientific Computing&\cr -\+&SIOPT&SIAM Journal on Optimization&\cr -\+&SIAP&SIAM Journal on Applied Mathematics&\cr -\+&SICON&SIAM Journal on Control and Optimization&\cr -\+&SIDMA&SIAM Journal on Discrete Mathematics&\cr -\+&TVP&Theory of Probability and Its Applications&\cr -\hbox to \hsize{\hrulefill} -\endinsert - -\Refs -\ref - \no 1 - \by L. A. Caffarelli and A. Friedman - \paper Regularity of the free boundary of a gas flow in an - $n$-dimensional porous medium - \jour Indiana Math. J. - \vol 29 - \yr 1980 - \pages 361--391 -\endref -\ref\no 2 - \by R. DeVore and B. Lucier - \paper High order regularity for solutions of the inviscid Burgers equation - \inbook Nonlinear Hyperbolic Problems -\procinfo Proceedings of an Advanced Research Workshop, Bordeaux, -France, June 1988 - \bookinfo Lecture Notes in Mathematics - \vol 1402 - \eds C. Carasso, P. Charrier, B. Hanouzet, and J.-L. Joly - \yr 1989 - \publ Springer-Verlag - \publaddr New York - \pages 147--154 -\endref -\ref \no 3 - \bysame - \paper Wavelets - \jour Acta Numerica - \yr 1992 - \ed A. Iserles - \publ Cambridge University Press - \publaddr New York - \pages 1--56 -\endref -\ref \no 4 - \by R. A. DeVore and V. A. Popov - \paper Interpolation spaces and non-linear approximation - \inbook Function Spaces and Applications - \bookinfo Lecture Notes in Mathematics - \procinfo Proceedings of the US--Swedish Seminar held in Lund, -Sweden, June 15--21, 1986 - \vol 1302 - \eds M. Cwikel, J. Peetre, Y. Sagher, and H. Wallin - \publ Springer-Verlag - \publaddr New York - \yr 1988 - \pages 191--205 - \endref -\ref \no 5 - \by R. A. DeVore and X. M. Yu - \paper Nonlinear $n$-widths in Besov spaces - \inbook Approximation Theory VI: Vol. 1 - \eds C. K. Chui, L. L. Schumaker, and J. D. Ward - \publ Academic Press - \publaddr New York - \yr 1989 - \pages 203--206 - \lang In Russian - \endref -\ref - \no 6 - \by K. Hollig and M. Pilant - \paper Regularity of the free boundary for the porous medium equation - \paperinfo MRC Tech. Rep. 2742 -\endref -\ref - \no 7 - \by J. Jerome - \book Approximation of Nonlinear Evolution Systems - \publ Academic Press - \publaddr New York - \yr 1983 -\endref -\ref - \no 8 - \manyby R. J. LeVeque - \paper Convergence of a large time step generalization of Godunov's method - for conservation laws - \jour Comm. Pure Appl. Math. - \vol 37 - \yr 1984 - \pages 463--478 -\endref -\ref\no 9 - \by O. Rioul and M. Vetterli - \paper Wavelets and signal processing - \jour IEEE Signal Processing Magazine - \vol 8 - \issue 4 - \yr 1991 - \toappear -\endref -\endRefs -\enddocument - diff --git a/Master/texmf-dist/doc/latex/siam/READ.ME b/Master/texmf-dist/doc/latex/siam/READ.ME deleted file mode 100644 index d362d373370..00000000000 --- a/Master/texmf-dist/doc/latex/siam/READ.ME +++ /dev/null @@ -1,38 +0,0 @@ -READ.ME 12/11/92 - -The following files constitute the full distribution -of SIAM's LaTeX macro package. The files are: - -read.me -siamltex.sty -docultex.tex -siam10.sty -siam11.sty -numinsec.sty -subeqn.sty -siam.bst -lexample.tex - -docultex.tex is the documentation file and should be refered to -for information about using the macros. - -Lines 339, 340, 348, 349, and 351 of siamltex.sty need to be -commented out to work with the NFSS. - -The SIAM macro's home is NETLIB@research.att.com, accessible through email. - -Both the LaTeX and plain TeX macros can be accessed through NETLIB: -Send an e-mail message to netlib@research.att.com, the body of the -message should be: - - send siamltex.all from typesetting - -for the LaTeX version, and - - send siamptex.all from typesetting - -for the plain TeX version. - -Questions, problems, bugs, and bug fixes should be -forwarded to SIAM TeX Support, 3600 University City Science Center, -Philadelphia PA, 19104. E-mail to duggan@siam.org. diff --git a/Master/texmf-dist/doc/latex/siam/docultex.tex b/Master/texmf-dist/doc/latex/siam/docultex.tex deleted file mode 100644 index 811a058cc91..00000000000 --- a/Master/texmf-dist/doc/latex/siam/docultex.tex +++ /dev/null @@ -1,592 +0,0 @@ -%% -%% This is file `docultex.tex', -%% Documentation for siam macros for use with LaTeX 2e -%% -%% By Paul Duggan for the Society for Industrial and Applied -%% Mathematics. -%% -%% December 1, 1995 -%% -%% Version 1.0a -%% -%% You are not allowed to change this file. -%% -%% You are allowed to distribute this file under the condition that -%% it is distributed together with all of the files in the siam macro -%% distribution. These are: -%% -%% siamltex.cls (main LaTeX macro for SIAM) -%% siamltex.sty (includes siamltex.cls for compatibility mode) -%% siam10.clo (size option for 10pt papers) -%% subeqn.clo (allows equation numbners with lettered subelements) -%% siam.bst (bibliographic style file for BibTeX) -%% docultex.tex (this file) -%% lexample.tex (example file for latex macro) -%% -%% If you receive only some of these files from someone, complain! -%% -%% You are NOT ALLOWED to distribute this file alone. You are NOT -%% ALLOWED to take money for the distribution or use of either this -%% file or a changed version, except for a nominal charge for copying -%% etc. -%% \CharacterTable -%% {Upper-case \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z -%% Lower-case \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z -%% Digits \0\1\2\3\4\5\6\7\8\9 -%% Exclamation \! Double quote \" Hash (number) \# -%% Dollar \$ Percent \% Ampersand \& -%% Acute accent \' Left paren \( Right paren \) -%% Asterisk \* Plus \+ Comma \, -%% Minus \- Point \. Solidus \/ -%% Colon \: Semicolon \; Less than \< -%% Equals \= Greater than \> Question mark \? -%% Commercial at \@ Left bracket \[ Backslash \\ -%% Right bracket \] Circumflex \^ Underscore \_ -%% Grave accent \` Left brace \{ Vertical bar \| -%% Right brace \} Tilde \~} - -\documentclass[final]{siamltex} - -\title{USING SIAM'S \LaTeX\ MACROS\thanks{This work was -supported by the Society for Industrial and Applied -Mathematics}} - -\author{Paul Duggan\thanks{Society for Industrial and -Applied Mathematics, Philadelphia, Pennsylvania. -(duggan@siam. org). Questions, comments, or corrections -to this document may be directed to that email address.}} - - -\begin{document} -\maketitle - -\begin{abstract} -Documentation is given for use of the SIAM \LaTeX\ macros. These -macros are now compatible with \LaTeX$2_{\varepsilon}$. -Instructions and suggestions for compliance with SIAM style -standards are also included. Familiarity with standard \LaTeX\ commands -is assumed. -\end{abstract} - -\begin{keywords}\end{keywords} - -\begin{AMS}\end{AMS} - - -\pagestyle{myheadings} -\thispagestyle{plain} -\markboth{PAUL DUGGAN}{USING SIAM'S \LaTeX\ MACROS} - -\section{Introduction} - -This file is documentation for the SIAM \LaTeX\ macros, and -provides instruction for submission of your files. - -To accommodate authors who electronically typeset their manuscripts, -SIAM supports the use of \LaTeX. To ensure quality typesetting according -to SIAM style standards, SIAM provides a \LaTeX\ macro style file. -Using \LaTeX\ to format a manuscript should simplify the editorial process -and lessen the author's proofreading burden. However, -it is still necessary to proofread the galley proofs with care. - -Electronic files should not be submitted until the paper has been -accepted, and then not until requested to do so by someone in the SIAM -office. Once an article is slated for an issue, -someone from the SIAM office will contact the author about any or all -of the following: editorial and stylistic queries, -supplying the source files (and any supplementary macros) -for the properly formatted article, and handling figures. - -When submitting electronic files (electronic submissions) -(to {\tt tex@siam.org}) include the journal, issue, and author's -name in the subject line of the message. -Authors are responsible for ensuring that the paper generated -from the source files exactly matches the paper that -was accepted for publication by the review editor. If it does not, -information on how it differs should be indicated in the transmission -of the file. When submitting a file, please be sure to include any -additional macros (other than those provided by SIAM) that will be -needed to run the paper. - -SIAM uses MS-DOS-based computers for \LaTeX\ processing. Therefore -all filenames should be restricted to eight characters or less, -plus a three character extension. - -Once the files are corrected here at SIAM, we will mail the revised -proofs to be read against the original edited hardcopy -manuscript. We are not -set up to shuttle back and forth varying electronic versions of each -paper, so we must rely on hard copy of the galleys. The author's proofreading -is an important but easily overlooked step. Even if SIAM were not -to introduce a single editorial change into your manuscript, there -would still be a need to check, because electronic transmission -can introduce errors. - -The distribution contains the following items: {\tt -siamltex.cls}, the main macro package based on {\tt -article.cls}; {\tt siam10.clo}, for the ten-point size option;\linebreak -{\tt subeqn.clo}, a style option for equation numbering (see \S3 for -an explanation); and {\tt siam.bst}, - the style file for use with {\sc Bib}\TeX. Also included are this -file {\tt docultex.tex} and a sample file {\tt lexample.tex}. -The sample file represents a standard application of -the macros. The rest of this paper will highlight -some keys to effective macro use, as well as point out options and -special cases, and describe SIAM style standards to which -authors should conform. - - -\section{Headings} -The top matter of a journal paper falls into a standard -format. It begins of course with the \verb|\documentclass| command - -\begin{verbatim} - -\documentclass{siamltex} - -\end{verbatim} - -Other class options can be included -in the bracketed argument of the command, separated by commas. - - -The title and author parts are formatted using the -\verb|\title| and \verb|\author| commands as described in Lamport -\cite{Lamport}. The \verb|\date| -command is not used. \verb|\maketitle| produces the actual -output of the commands. - -The addresses and support acknowledgments are put into the -\verb|\author| commands via \verb|\thanks|. If support is -overall for the authors, the support acknowledgment should -be put in a \verb|\thanks| command in the \verb|\title|. -Specific support should go following the addresses of the -individual authors in the same \verb|\thanks| command. - -Sometimes authors have support or addresses in common which -necessitates having multiple \verb|\thanks| commands for -each author. Unfortunately \LaTeX\ does not normally allow this, -so a special procedure must be used. An example of this procedure -follows. Grant information can also be run into both authors' -footnotes. - -\begin{verbatim} - -\title{TITLE OF PAPER} - -\author{A.~U. Thorone\footnotemark[2]\ \footnotemark[5] -\and A.~U. Thortwo\footnotemark[3]\ \footnotemark[5] -\and A.~U. Thorthree\footnotemark[4]} - -\begin{document} -\maketitle - -\renewcommand{\thefootnote}{\fnsymbol{footnote}} - -\footnotetext[2]{Address of A.~U. Thorone} -\footnotetext[3]{Address of A.~U. Thortwo} -\footnotetext[4]{Address of A.~U. Thorthree} -\footnotetext[5]{Support in common for the first and second -authors.} - -\renewcommand{\thefootnote}{\arabic{footnote}} - -\end{verbatim} - -Notice that the footnote marks begin with {\tt [2]} -because the first mark (the asterisk) will be used in the -title for date-received information by SIAM, even if not -already used for support data. This is just one example; -other situations follow a similar pattern. - -Following the author and title is the abstract, key words -listing, and AMS subject classification number(s), -designated using the \verb|{abstract}|, \verb|{keywords}|, -and \verb|{AMS}| environments. If -there is only one AMS number, the commands -\verb|\begin{AM}| and \verb|\end{AM}| are used -instead of \verb|{AMS}|. This causes the heading to be -in the singular. Authors are responsible for providing AMS numbers. -They can be found in the Annual Index of Math Reviews, or -through {\tt e-Math} ({\tt telnet e-math.ams.com}; login -and password are both {\tt e-math}). - -Left and right running heads should be provided in the -following way. - -\begin{verbatim} - -\pagestyle{myheadings} -\thispagestyle{plain} -\markboth{A.~U. THORONE AND A.~U. THORTWO}{SHORTER PAPER -TITLE} - -\end{verbatim} - -\section{Equations and mathematics} - -One advantage of \LaTeX\ is that it can automatically number -equations and refer to these equation numbers in text. While plain \TeX's -method of equation numbering (explicit numbering using -\verb|\leqno|) works in the SIAM macro, it is not preferred -except in certain cases. SIAM style guidelines call for -aligned equations in many circumstances, and \LaTeX's -\verb|{eqnarray}| environment is not compatible with -\verb|\leqno| and \LaTeX\ is not compatible with the plain -\TeX\ command \verb|\eqalign| and \verb|\leqalignno|. Since -SIAM may have to alter or realign certain groups of -equations, it is necessary to use the \LaTeX\ system of -automatic numbering. - -Sometimes it is desirable to designate subequations of a larger -equation number. The subequations are designated with -(roman font) letters appended after the number. SIAM has -supplemented its macros with the {\tt subeqn.clo} option which -defines the environment \verb|{subequations}|. - -\begin{verbatim} - -\begin{subequations}\label{EKx} -\begin{equation} - y_k = B y_{k-1} + f, \qquad k=1,2,3,\ldots -\end{equation} -for any initial vector $ y_0$. Then -\begin{equation} - y_k\rightarrow u \mbox{\quad iff\quad} \rho( B)<1. -\end{equation} -\end{subequations} - -\end{verbatim} - -All equations within the \verb|{subequations}| environment -will keep the same overall number, but the letter -designation will increase. - -Clear equation formatting using \TeX\ can be challenging. Aside from -the regular \TeX\ documentation, authors will find Nicholas -J. Higham's book {\em Handbook of Writing for the Mathematical -Sciences\/} \cite{Higham} useful for guidelines and tips on -formatting with \TeX. The book covers many other topics related -to article writing as well. - -Authors commonly make mistakes by using - \verb|<|, \verb|>|, \verb|\mid|, and -\verb|\parallel| as delimiters, instead of -\verb|\langle|, \verb|\rangle|, \verb:|:, -and \verb:\|:. The incorrect symbols have particular -meanings distinct from the correct ones and should not be confused. - -\begin{table}[htbp] -\caption{Illustration of incorrect delimiter use.} -\begin{center}\footnotesize -\renewcommand{\arraystretch}{1.3} -\begin{tabular}{|ll|ll|}\hline -\multicolumn{2}{|c|}{{\bf Wrong}} & \multicolumn{2}{c|}{{\bf Right}}\\ \hline -\verb|<x, y>| & $<x, y>$ & \verb|\langle x, y\rangle| & $\langle x, y\rangle$\\ -\verb|5 < \mid A \mid| & $5 < \mid A \mid$ & \verb:5 < |A|: & $5 < |A|$\\ -\verb|6x = \parallel x|&&&\\ -\verb| - 1\parallel_{i}| & $6x = \parallel x - 1\parallel_{i}$ & - \verb:6x = \|x - 1\|_{i}: & $6x = \| x - 1\|_{i}$\\ \hline -\end{tabular} -\end{center} -\end{table} - -Another common author error is to put large (and even medium sized) -matrices in-line with the text, rather than displaying them. This -creates unattractive line spacing problems, and should be assiduously -avoided. Text-sized matrices (like $({a \atop b} {b \atop c})$) might -be used but anything much more complex than the example cited will -not be easy to read and should be displayed. - -More information on the formatting of equations and aligned -equations is found in Lamport \cite{Lamport}. Authors bear -primary responsibility for formatting their equations within -margins and in an aesthetically pleasing and informative manner. - -The SIAM macros include additional roman math words, or ``log-like" -functions, to those provided in standard \TeX. The following -commands are added: \verb:\const:, \verb:\diag:, \verb:\grad:, -\verb:\Range:, \verb:\rank:, and \verb:\supp:. -These commands produce the same word as the command name -in math mode, in upright type. - -\section{Special fonts} - -SIAM supports the use of the AMS-\TeX\ fonts (version 2.0 -and later). The package \verb|amsfonts| can be included with -the command\linebreak \verb|\usepackage{amsfonts}|. This package -is part of the AMS-\LaTeX distribution, available -from the AMS or from the Comprehensive TeX Archive -Network (anonymous ftp to ftp.shsu.edu). The blackboard bold font in this -font package can be used for designating number sets. -This is preferable to other methods of combining letters -(such as I and R for the real numbers) to produce pseudo-bold -letters but this is tolerable as well. Typographically speaking, -number sets may simply be designated using regular bold letters; -the blackboard bold typeface was designed to fulfil a desire -to simulate the limitations of a chalk board in printed type. - - -\subsection{Punctuation} -All standard punctuation and all numerals should be set in roman type -(upright) even within italic text. The only exceptions are periods and -commas. They may be set to match the surrounding text. - -References to sections should use the symbol \S, generated by -\verb|\S|. (If the reference begins a sentence, the term ``Section'' -should be spelled out in full.) Authors should not redefine -\verb|\S|, say, to be a calligraphic S, because \verb|\S| -must be reserved for use as the section symbol. - -Authors sometimes confuse the use of various types of dashes. -Hyphens (\verb|-|, -) are used for some compound words (many -such words should have no hyphen but must be run together, -like ``nonzero,'' or split apart, like ``well defined''). -Minus signs (\verb|$-$|, $-$) -should be used in math to represent subtraction or negative numbers. -En dashes (\verb|--|, --) are used for ranges (like 3--5, -June--August), or for joined names (like Runge--Kutta). Em dashes -(\verb|---|, ---) are used to set off a clause---such as this -one---from the rest of the sentence. - - -\subsection{Text formatting} - -SIAM style preferences do not make regular use of the \verb|{enumerate}| -and \verb|{itemize}| environments. Instead, -{\tt siamltex.cls} includes definitions of two alternate list -environments, \verb|{remunerate}| and \verb|{romannum}|. -Unlike the standard itemized lists, these environments do -not indent the secondary lines of text. The labels, whether -defaults or the optional user-defined, are always aligned -flush right. - -The \verb|{remunerate}| environment consecutively numbers -each item with an arabic numeral followed by a period. This -number is always upright, even in slanted -environments. (For those wondering at the unusual -naming of this environment, it comes from Seroul and Levy's -\cite{SerLev} definition of a similar macro for plain \TeX: -%{\tt \char"5C meti} -\verb|\meti| which is -% {\tt \char"5C item} -\protect\verb|\item| spelled backwards. Thus -%{\tt \{remunerate\}}, -\verb|{remunerate}| -a portion of -%{\tt \{enumerate\}} -\verb|{enumerate}| -spelled backwards.) - -The \verb|{romannum}| environment consecutively numbers -each item with a lower-case roman numeral enclosed in -parentheses. This number will always be upright within -slanted environments (as in theorems). - - -\section{Theorems and Lemmas} -Theorems, lemmas, corollaries, definitions, and propositions are covered -in the SIAM macros by the theorem-environments -\verb|{theorem}|, \verb|{lemma}|, \verb|{corollary}|, -\verb|{definition}| and \verb|{proposition}|. These are all -numbered in the same sequence and produce labels in small -caps with an italic body. Other environments may be specified by the -\verb|\newtheorem| command. SIAM's style is for Remarks and Examples -to appear with italic labels and an upright roman body. - -\begin{verbatim} - -\begin{theorem} -Sample theorem included for illustration. -Numbers and parentheses, like equation $(3.2)$, should be set -in roman type. Note that words (as opposed to ``log-like'' -functions) in displayed equations, such as -$$ x^2 = Y^2 \sin z^2 \mbox{ for all } x $$ -will appear in italic type in a theorem, though normally -they should appear in roman.\end{theorem} - -\end{verbatim} - -This sample produces Theorem 4.1 below. - -\begin{theorem} -Sample theorem included for illustration. -Numbers and parentheses, like equation $(3.2)$, should be set -in roman type. Note that words (as opposed to ``log-like'' -functions) in displayed equations, such as -$$ x^2 = Y^2 \sin z^2 \mbox{ for all } x $$ -will appear in italic type in a theorem, though normally -they should appear in roman. -\end{theorem} - - -Proofs are handled with the \verb|\begin{proof}| -\verb|\end{proof}| environment. A ``QED'' box \endproof\ is created -automatically by \verb|\end{proof}|, but this should be -preceded with a \verb|\qquad|. - -Named proofs, if used, must be done independently by the -authors. SIAM style specifies that proofs which end with -displayed equations should have the QED box two ems (\verb|\qquad|) -from the end of the equation on line with it horizontally. -Below is an example of how this can be done: - -\begin{verbatim} - -{\em Proof}. Proof of the previous theorem - . - . - . -thus, -$$ -a^2 + b^2 = c^2 \qquad\endproof -$$ - -\end{verbatim} - - -\section{Figures and tables} -Figures and tables sometimes require special consideration. -Tables in SIAM style are need to be set in eight point size -by using the \verb|\footnotesize| command inside the -\verb|\begin{table}| environment. Also, they should be designed -so that they do not extend beyond the text margins. - -SIAM style requires that no figures or tables appear in the -references section of the paper. \LaTeX\ is notorious for -making figure placement difficult, so it is important to -pay particular attention to figure placement near the -references in the text. All figures and tables should -be referred to in the text. - -SIAM supports the use of {\tt epsfig} for including {\sc PostScript} -figures. All {\sc Post\-Script} figures should be sent in separate -files. See the {\tt epsfig} documentation (available via -anonymous ftp from CTAN: ftp.shsu.edu) for more details on the use -of this style option. It is a good idea to submit high-quality -hardcopy of all {\sc Post\-Script} figures just in case there -is difficulty in the reproduction of the figure. Figures produced -by other non-\TeX\ methods should be included as high-quality -hardcopy when the manuscript is submitted. - -{\sc PostScript} figures that are sent should be generated with -sufficient line thickness. Some past figures authors have sent -had their line widths become very faint when SIAM set the papers -using a high-quality 1200dpi printer. - -Hardcopy for non-{\sc PostScript} figures should be included in -the submission of the hardcopy of the manuscript. Space -should be left in the \verb|{figure}| command for the -hardcopy to be inserted in production. - -\section{Bibliography and Bib\TeX} - -If using {\sc Bib}\TeX, authors need not submit the {\tt .bib} file for -their papers. Merely submit the completed {\tt .bbl} file, having used -{\tt siam.bst} as their bibliographic style file. {\tt siam.bst} -only works with Bib\TeX\ version 99i and later. The use of -Bib\TeX\ and the preparation of a {\tt .bib} file is -described in greater detail in \cite{Lamport}. - -If not using Bib\TeX, SIAM bibliographic references follow -the format of the following examples: - -\begin{verbatim} - -\bibitem{Ri} {\sc W. Riter}, -{\em Title of a paper appearing in a book}, in The Book -Title, E.~D. One, E.~D. Two, and A.~N. Othereditor, eds., -Publisher, Location, 1992, pp.~000--000. - -\bibitem{AuTh1} {\sc A.~U. Thorone}, {\em Title of paper -with lower case letters}, SIAM J. Abbrev. Correctly, 2 -(1992), pp.~000--000. - -\bibitem{A1A2} {\sc A.~U. Thorone and A.~U. Thortwo}, {\em -Title of paper appearing in book}, in Book Title: With All -Initial Caps, Publisher, Location, 1992. - -\bibitem{A1A22} \sameauthor, % generates the 3 em rule -{\em Title of Book{\rm :} Note Initial Caps and {\rm ROMAN -TYPE} for Punctuation and Acronyms}, Publisher, -Location, pp.~000--000, 1992. - -\bibitem{AuTh3} {\sc A.~U. Thorthree}, {\em Title of paper -that's not published yet}, SIAM. J. Abbrev. Correctly, to appear. - -\end{verbatim} - -Other types of references fall into the same general -pattern. See the sample file or any SIAM journal for other -examples. Authors must correctly format their bibliography to -be considered as having used the macros correctly. An incorrectly -formatted bibliography is not only time-consuming for SIAM to -process but it is possible that errors may be introduced into -it by keyboarders/copy editors. - -As an alternative to the above style of reference, an alphanumeric -code may be used in place of the number (e.g., [AUTh90]). The same -commands are used, but \verb|\bibitem| takes an optional argument -containing the desired alphanumeric code. - -Another alternative is no number, simply the authors' names and -the year of publication following in parentheses. The rest of the -format is identical. The macros do not support this alternative -directly, but modifications to the macro definition are possible -if this reference style is preferred. - - -\section{Conclusion} Many other style suggestions and tips -could be given to help authors but are beyond the scope of this -document. Simple mistakes can be avoided by increasing your familiarity -with how \LaTeX\ functions. The books referred to throughout this document -are also useful to the author who wants clear, beautiful typography -with minimal mistakes. - -\Appendix -\section{The use of appendices} -The \verb|\appendix| command may be used before the final sections -of a paper to designate them as appendices. Once \verb|\appendix| -is called, all subsequent sections will appear as - -\appendix -\section{Title of appendix} Each one will be sequentially lettered -instead of numbered. Theorem-like environments, subsections, -and equations will also have the section number changed to a letter. - -If there is only {\em one} appendix, however, the \verb|\Appendix| -(with a capital letter) should be used instead. This produces only -the word {\bf Appendix} in the section title, and does not add a letter. -Equation numbers, theorem numbers and subsections of the appendix -will have the letter ``A'' designating the section number. - -If you don't want to title your appendix, and just call it -{\bf Appendix A.} for example, use \verb|\appendix\section*{}| -and don't include anything in the title field. This works -opposite to the way \verb|\section*| usually works, by including the -section number, but not using a title. - - -Appendices should appear before the bibliography section, not after, -and any acknowledgments should be placed after the appendices and before -the bibliography. - -\begin{thebibliography}{1} -\bibitem{GoMiSa} {\sc M. Goossens, F. Mittelbach, and A. Samarin}, -{\em The} \LaTeX\ {\em Companion}, Addison-Wesley, Reading, MA, 1994. - -\bibitem{Higham} {\sc N.~J. Higham}, {\em Handbook of Writing for -the Mathematical Sciences}, Society for Industrial and Applied -Mathematics, Philadelphia, PA, 1993. - -\bibitem{Lamport} {\sc L. Lamport}, \LaTeX: {\em A Document -Preparation System}, Addison-Wesley, Reading, MA, 1986. - -\bibitem{SerLev} {\sc R. Seroul and S. Levy}, {\em A -Beginner's Book of} \TeX, Springer-Verlag, Berlin, New -York, 1991. -\end{thebibliography} - - -\end{document} -%% end of file `docultex.tex'
\ No newline at end of file diff --git a/Master/texmf-dist/doc/latex/siam/lexample.tex b/Master/texmf-dist/doc/latex/siam/lexample.tex deleted file mode 100644 index a8502d3788a..00000000000 --- a/Master/texmf-dist/doc/latex/siam/lexample.tex +++ /dev/null @@ -1,658 +0,0 @@ -%% -%% This is file `lexample.tex', -%% Sample file for siam macros for use with LaTeX 2e -%% -%% By Paul Duggan for the Society for Industrial and Applied -%% Mathematics. -%% -%% October 1, 1995 -%% -%% Version 1.0 -%% -%% You are not allowed to change this file. -%% -%% You are allowed to distribute this file under the condition that -%% it is distributed together with all of the files in the siam macro -%% distribution. These are: -%% -%% siamltex.cls (main LaTeX macro file for SIAM) -%% siamltex.sty (includes siamltex.cls for compatibility mode) -%% siam10.clo (size option for 10pt papers) -%% subeqn.clo (allows equation numbners with lettered subelements) -%% siam.bst (bibliographic style file for BibTeX) -%% docultex.tex (documentation file) -%% lexample.tex (this file) -%% -%% If you receive only some of these files from someone, complain! -%% -%% You are NOT ALLOWED to distribute this file alone. You are NOT -%% ALLOWED to take money for the distribution or use of either this -%% file or a changed version, except for a nominal charge for copying -%% etc. -%% \CharacterTable -%% {Upper-case \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z -%% Lower-case \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z -%% Digits \0\1\2\3\4\5\6\7\8\9 -%% Exclamation \! Double quote \" Hash (number) \# -%% Dollar \$ Percent \% Ampersand \& -%% Acute accent \' Left paren \( Right paren \) -%% Asterisk \* Plus \+ Comma \, -%% Minus \- Point \. Solidus \/ -%% Colon \: Semicolon \; Less than \< -%% Equals \= Greater than \> Question mark \? -%% Commercial at \@ Left bracket \[ Backslash \\ -%% Right bracket \] Circumflex \^ Underscore \_ -%% Grave accent \` Left brace \{ Vertical bar \| -%% Right brace \} Tilde \~} - - -\documentclass[final]{siamltex} - -% definitions used by included articles, reproduced here for -% educational benefit, and to minimize alterations needed to be made -% in developing this sample file. - -\newcommand{\pe}{\psi} -\def\d{\delta} -\def\ds{\displaystyle} -\def\e{{\epsilon}} -\def\eb{\bar{\eta}} -\def\enorm#1{\|#1\|_2} -\def\Fp{F^\prime} -\def\fishpack{{FISHPACK}} -\def\fortran{{FORTRAN}} -\def\gmres{{GMRES}} -\def\gmresm{{\rm GMRES($m$)}} -\def\Kc{{\cal K}} -\def\norm#1{\|#1\|} -\def\wb{{\bar w}} -\def\zb{{\bar z}} - -% some definitions of bold math italics to make typing easier. -% They are used in the corollary. - -\def\bfE{\mbox{\boldmath$E$}} -\def\bfG{\mbox{\boldmath$G$}} - -\title{Sample file for SIAM \LaTeX\ macro package\thanks{This - work was supported by the Society for Industrial and - Applied Mathematics, Philadelphia, Pennsylvania.}} - -% The thanks line in the title should be filled in if there is -% any support acknowledgement for the overall work to be included -% This \thanks is also used for the received by date info, but -% authors are not expected to provide this. - -\author{Paul Duggan\thanks{Composition Department, Society - for Industrial and Applied Mathematics, 3600 Univeristy - City Science Center, Philadelphia, Pennsylvania, - 19104-2688 ({\tt duggan@siam.org}).} - \and Various A.~U. Thors\thanks{Various Affiliations, - supported by various foundation grants.}} - -\begin{document} - -\maketitle - -\begin{abstract} -An example of SIAM \LaTeX\ macros is presented. Various -aspects of composing manuscripts for SIAM's journal series -are illustrated with actual examples from accepted -manuscripts. SIAM's stylistic standards are adhered to -throughout, and illustrated. -\end{abstract} - -\begin{keywords} -sign-nonsingular matrix, LU-factorization, indicator -polynomial -\end{keywords} - -\begin{AMS} -15A15, 15A09, 15A23 -\end{AMS} - -\pagestyle{myheadings} -\thispagestyle{plain} -\markboth{P. DUGGAN AND V. A. U. THORS}{SIAM MACRO EXAMPLES} - - -\section{Introduction and examples} -This paper presents a sample file for the use of SIAM's -\LaTeX\ macro package. It illustrates the features of the -macro package, using actual examples culled from various -papers published in SIAM's journals. It is to be expected -that this sample will provide examples of how to use the -macros to generate standard elements of journal papers, -e.g., theorems, definitions, or figures. This paper also -serves as an example of SIAM's stylistic preferences for -the formatting of such elements as bibliographic references, -displayed equations, and equation arrays, among others. -Some special circumstances are not dealt with in this -sample file; for such information one should see the -included documentation file. - -{\em Note:} This paper is not to be read in any form for content. -The conglomeration of equations, lemmas, and other text elements were -put together solely for typographic illustrative purposes and don't -make any sense as lemmas, equations, etc. - -\subsection{Sample text} -Let $S=[s_{ij}]$ ($1\leq i,j\leq n$) be a $(0,1,-1)$-matrix -of order $n$. Then $S$ is a {\em sign-nonsingular matrix} -(SNS-matrix) provided that each real matrix with the same -sign pattern as $S$ is nonsingular. There has been -considerable recent interest in constructing and -characterizing SNS-matrices \cite{bs}, \cite{klm}. There -has also been interest in strong forms of -sign-nonsingularity \cite{djd}. In this paper we give a new -generalization of SNS-matrices and investigate some of -their basic properties. - -Let $S=[s_{ij}]$ be a $(0,1,-1)$-matrix of order $n$ and -let $C=[c_{ij}]$ be a real matrix of order $n$. The pair -$(S,C)$ is called a {\em matrix pair of order} $n$. -Throughout, $X=[x_{ij}]$ denotes a matrix of order $n$ -whose entries are algebraically independent indeterminates -over the real field. Let $S\circ X$ denote the Hadamard -product (entrywise product) of $S$ and $X$. We say that the -pair $(S,C)$ is a {\em sign-nonsingular matrix pair of -order} $n$, abbreviated SNS-{\em matrix pair of order} $n$, -provided that the matrix \[A=S\circ X+C\] is nonsingular -for all positive real values of the $x_{ij}$. If $C=O$ -then the pair $(S,O)$ is a SNS-matrix pair if and only if -$S$ is a SNS-matrix. If $S=O$ then the pair $(O,C)$ is a -SNS-matrix pair if and only if $C$ is nonsingular. Thus -SNS-matrix pairs include both nonsingular matrices and -sign-nonsingular matrices as special cases. - -The pairs $(S,C)$ with -\[S=\left[\begin{array}{cc}1&0\\0&0\end{array}\right],\qquad -C=\left[\begin{array}{cc}1&1\\1&1\end{array}\right]\] and -\[S=\left[\begin{array}{ccc}1&1&0\\1&1&0\\0&0&0\end{array}\right],\qquad -C=\left[\begin{array}{ccc}0&0&1\\0&2&0\\ -3&0&0\end{array}\right]\] are examples of SNS-matrix pairs. - -\subsection{A remuneration list} -In this paper we consider the evaluation of integrals of the -following forms: -\begin{equation} -\int_a^b \left( \sum_i E_i B_{i,k,x}(t) \right) - \left( \sum_j F_j B_{j,l,y}(t) \right) dt,\label{problem} -\end{equation} -\begin{equation} -\int_a^b f(t) \left( \sum_i E_i B_{i,k,x}(t) \right) dt,\label{problem2} -\end{equation} -where $B_{i,k,x}$ is the $i$th B-spline of order $k$ defined over the -knots $x_i, x_{i+1}, \ldots, x_{i+k}$. -We will consider B-splines normalized so that their integral is one. -The splines may be of different orders and -defined on different knot sequences $x$ and $y$. -Often the limits of integration will be the entire real line, $-\infty$ -to $+\infty$. Note that (\ref{problem}) is a special case of (\ref{problem2}) -where $f(t)$ is a spline. - - -There are five different methods for calculating (\ref{problem}) -that will be considered: -\begin{remunerate} -\item Use Gauss quadrature on each interval. -\item Convert the integral to a linear combination of - integrals of products of B-splines and provide a recurrence for - integrating the product of a pair of B-splines. -\item Convert the sums of B-splines to piecewise - B\'{e}zier format and integrate segment - by segment using the properties of the Bernstein polynomials. -\item Express the product of a pair of B-splines as a linear combination - of B-splines. - Use this to reformulate the integrand as a linear combination - of B-splines, and integrate term by term. -\item Integrate by parts. -\end{remunerate} -Of these five, only methods 1 and 5 are suitable for calculating -(\ref{problem2}). The first four methods will be touched on and the -last will be discussed at length. - - -\subsection{Some displayed equations and \{{\tt eqnarray}\}s} - By introducing the product topology on $R^{m \times m} \times -R^{n \times n}$ with the induced inner product -\begin{equation} -\langle (A_{1},B_{1}), (A_{2},B_{2})\rangle := \langle A_{1},A_{2}\rangle -+ \langle B_{1},B_{2}\rangle,\label{eq2.10} -\end{equation} -we calculate the Fr\'{e}chet derivative of $F$ as follows: -\begin{eqnarray} - F'(U,V)(H,K) &=& \langle R(U,V),H\Sigma V^{T} + U\Sigma K^{T} - -P(H\Sigma V^{T} + U\Sigma K^{T})\rangle \nonumber \\ - &=& \langle R(U,V),H\Sigma V^{T} + U\Sigma K^{T}\rangle \label{eq2.11} \\ -&=& \langle R(U,V)V\Sigma^{T},H\rangle + \langle \Sigma^{T}U^{T}R(U,V),K^{T}\rangle. \nonumber -\end{eqnarray} -In the middle line of (\ref{eq2.11}) we have used the fact that the range of -$R$ is always perpendicular to the range of $P$. The gradient $\nabla F$ of -$F$, therefore, may be interpreted as the -pair of matrices: -\begin{equation} - \nabla F(U,V) = (R(U,V)V\Sigma^{T},R(U,V)^{T}U\Sigma ) \in -R^{m \times m} \times R^{n \times n}. \label{eq2.12} -\end{equation} -Because of the product topology, we know -\begin{equation} - {\cal T}_{(U,V)}({\cal O} (m) \times {\cal O} (n)) = -{\cal T}_{U}{\cal O} (m) \times {\cal T}_{V}{\cal O} (n), \label{eq2.13} -\end{equation} -where ${\cal T}_{(U,V)}({\cal O} (m) \times {\cal O} (n))$ stands for the -tangent space to the manifold ${\cal O} (m) \times {\cal O} (n)$ at $(U,V) -\in {\cal O} (m) \times {\cal O} (n)$ and so on. The projection of -$\nabla F(U,V)$ onto ${\cal T}_{(U,V)}({\cal O} (m) \times {\cal O} (n))$, -therefore, is the product of the projection of the first component of -$\nabla F(U,V)$ onto ${\cal T}_{U}{\cal O} (m)$ and the projection of the -second component of $\nabla F(U,V)$ onto ${\cal T}_{V}{\cal O} (n)$. -In particular, we claim that the -projection $ g(U,V)$ of the gradient $\nabla F(U,V)$ onto -${\cal T}_{(U,V)}({\cal O} (m) \times {\cal O} (n))$ is given by the pair of -matrices: -\begin{eqnarray} -g(U,V) = && \left( \frac{R(U,V)V\Sigma^{T}U^{T}-U\Sigma V^{T}R(U,V)^{T}}{2}U, -\right. \nonumber \\[-1.5ex] -\label{eq2.14}\\[-1.5ex] -&&\quad \left. \frac{R(U,V)^{T}U\Sigma V^{T}-V - \Sigma^{T}U^{T}R(U,V)}{2}V \right).\nonumber -\end{eqnarray} -Thus, the vector field -\begin{equation} -\frac{d(U,V)}{dt} = -g(U,V) \label{eq2.15} -\end{equation} -defines a steepest descent flow on the manifold ${\cal O} (m) \times -{\cal O} (n)$ for the objective function $F(U,V)$. - - -\section{Main results} - -Let $(S,C)$ be a matrix pair of order $n$. The determinant -\[\det (S\circ X+C)\] -is a polynomial in the indeterminates of $X$ of degree at -most $n$ over the real field. We call this polynomial the -{\em indicator polynomial} of the matrix pair $(S,C)$ -because of the following proposition. - -\begin{theorem} -\label{th:prop} -The matrix pair $(S,C)$ is a {\rm SNS}-matrix pair if and -only if all the nonzero coefficients in its indicator -polynomial have the same sign and there is at least one -nonzero coefficient. -\end{theorem} - -\begin{proof} -Assume that $(S,C)$ is a SNS-matrix pair. Clearly the -indicator polynomial has a nonzero coefficient. Consider a -monomial -\begin{equation} -\label{eq:mono} -b_{i_{1},\ldots,i_{k};j_{1},\ldots,j_{k}}x_{i_{1}j_{1}}\cdots -x_{i_{k}j_{k}} -\end{equation} -occurring in the indicator polynomial with a nonzero -coefficient. By taking the $x_{ij}$ that occur in -(\ref{eq:mono}) large and all others small, we see that any -monomial that occurs in the indicator polynomial with a -nonzero coefficient can be made to dominate all others. -Hence all the nonzero coefficients have the same sign. The -converse is im-\linebreak mediate. \qquad\end{proof} - - -For SNS-matrix pairs $(S,C)$ with $C=O$ the indicator -polynomial is a homogeneous polynomial of degree $n$. In -this case Theorem \ref{th:prop} is a standard fact about -SNS-matrices. - -\begin{lemma}[{\rm Stability}] -\label{stability} -Given $T>0$, suppose that $\| \epsilon (t) \|_{1,2} \leq h^{q-2}$ -for $0 \leq t \leq T$ and $q \geq 6$. -Then there exists a positive number $B$ that depends on -$T$ and the exact solution $\pe$ only such that for all $0 \leq t \leq T$, -\begin{equation} -\label{Gron} -\frac {d}{dt} \| \epsilon (t) \| _{1,2} \leq B - ( h^{q-3/2} + \| \epsilon (t) \|_{1,2})\;. -\end{equation} -The function $B(T)$ can be chosen to be nondecreasing in time. -\end{lemma} - - -\begin{theorem} -\label{th:gibson} -The maximum number of nonzero entries in a {\rm SNS}-matrix -$S$ of order $n$ equals \[\frac{n^{2}+3n-2}{2}\] with -equality if and only if there exist permutation matrices -such that $P|S|Q=T_{n}$ where -\begin{equation} -\label{eq:gibson} -T_{n}=\left[\begin{array}{cccccc} 1&1&\cdots&1&1&1\\ -1&1&\cdots&1&1&1\\ 0&1&\cdots&1&1&1\\ -\vdots&\vdots&\ddots&\vdots&\vdots&\vdots\\ -0&0&\cdots&1&1&1\\ 0&0&\cdots&0&1&1\end{array}\right]. -\end{equation} -\end{theorem} - -We note for later use that each submatrix of $T_{n}$ of -order $n-1$ has all 1s on its main diagonal. - -We now obtain a bound on the number of nonzero entries of -$S$ in a SNS-matrix pair $(S,C)$ in terms of the degree of -the indicator polynomial. We denote the strictly upper -triangular (0,1)-matrix of order $m$ with all 1s above the -main diagonal by $U_{m}$. The all 1s matrix of size $m$ by -$p$ is denoted by $J_{m,p}$. - - -\begin{proposition}[{\rm Convolution theorem}] -\label{pro:2.1} Let -\begin{eqnarray*} -a\ast u(t) = \int_0^t a(t- \tau) u(\tau) d\tau, \hspace{.2in} t \in -(0, \infty). -\end{eqnarray*} -Then -\begin{eqnarray*} -\widehat{a\ast u}(s) = \widehat{a}(s)\widehat{u}(s). -\end{eqnarray*} -\end{proposition} - -\begin{lemma} -\label{lem:3.1} -For $s_0 >0$, if -$$ -\int_0^{\infty} e^{-2s_0 t}v^{(1)}(t) v(t) dt \; \leq 0 \;, -$$ -then -\begin{eqnarray*} -\int_0^{\infty} e^{-2s_0 t} v^2(t) dt \; \leq \; \frac{1}{2s_0} v^2(0). -\end{eqnarray*} -\end{lemma} - -{\em Proof}. Applying integration by parts, we obtain -\begin{eqnarray*} -\int_0^{\infty} e^{-2s_0 t} [v^2(t)-v^2(0)] dt -&=&\lim_{t\rightarrow \infty}\left ( --\frac{1}{2s_0}e^{-2s_0 t}v^2(t) \right ) +\frac{1}{s_0} -\int_0^{\infty} e^{-2s_0 t}v^{(1)}(t)v(t)dt\\ -&\leq& \frac{1}{s_0} \int_0^{\infty} e^{-2s_0 t} v^{(1)}(t)v(t) dt \;\; -\leq \;\; 0. -\end{eqnarray*} -Thus -$$ -\int_0^{\infty} e^{-2s_0 t} v^2(t) dt \;\;\leq v^2(0) \int_0^{\infty} -\;\;e^{-2s_0 t} dt\;\;=\;\;\frac{1}{2s_0} v^2(0).\eqno\endproof -$$ - -\begin{corollary}\label{c4.1} -Let $ \bfE $ satisfy $(5)$--$(6)$ and -suppose $ \bfE^h $ satisfies $(7)$ and $(8)$ -with a general $ \bfG $. Let $ \bfG= \nabla \times {\bf \Phi} + \nabla p,$ -$p \in H_0^1 (\Omega) $. Suppose that $\nabla p$ and $ \nabla \times -{\bf \Phi} $ satisfy all the assumptions of Theorems $4.1$ and -$4.2$, respectively. In addition suppose all the regularity -assumptions of Theorems $4.1$--$4.2$ are satisfied. Then -for $ 0 \le t \le T $ and $ 0 < \epsilon \le \epsilon_0 $ there exists a -constant $ C = C(\epsilon, T) $ such that -$$ -\Vert (\bfE - \bfE^h)(t) \Vert_0 \le C h^{k+1- \epsilon}, -$$ -where $ C $ also depends on the constants given in Theorems -$4.1$ and $4.2$. -\end{corollary} - - -\begin{definition} -Let $S$ be an isolated invariant set with isolating neighborhood $N$. -An {\em index pair} for $S$ is a pair of compact sets $(N_{1},N_{0})$ -with $N_{0} \subset N_{1} \subset N$ such that: -\begin{romannum} -\item $cl(N_{1} \backslash N_{0})$ -is an isolating neighborhood for $S$. -\item $N_{i}$ is positively invariant relative to $N$ for $i=0,1$, -i.e., given -$x \in N_{i}$ and $x \cdot [0,t] \subset N$, then $x \cdot [0,t] \subset -N_{i}$. -\item $N_{0}$ is an exit set for $N_{1}$, i.e. if $x \in N_{1}$, -$x \cdot [0, \infty ) \not\subset N_{1}$, then there is a $T \geq 0$ such -that $x \cdot [0,T] \subset N_{1}$ and $x \cdot T \in N_{0}$. -\end{romannum} -\end{definition} - -\subsection{Numerical experiments} We conducted numerical experiments -in computing inexact Newton steps for discretizations of a -{\em modified Bratu problem}, given by -\begin{eqnarray} -{\ds \Delta w + c e^w + d{ {\partial w}\over{\partial x} } } -&=&{\ds f \quad {\rm in}\ D, }\nonumber\\[-1.5ex] -\label{bratu} \\[-1.5ex] -{\ds w }&=&{\ds 0 \quad {\rm on}\ \partial D , } \nonumber -\end{eqnarray} -where $c$ and $d$ are constants. The actual Bratu problem has $d=0$ and -$f \equiv0$. It provides a simplified model of nonlinear diffusion -phenomena, e.g., in combustion and semiconductors, and has been -considered by Glowinski, Keller, and Rheinhardt \cite{GloKR85}, -as well as by a number of other investigators; see \cite{GloKR85} -and the references therein. See also problem 3 by Glowinski and Keller -and problem 7 by Mittelmann in the collection of nonlinear model -problems assembled by Mor\'e \cite{More}. The modified problem -(\ref{bratu}) has been used as a test problem for inexact Newton -methods by Brown and Saad \cite{Brown-Saad1}. - -In our experiments, we took $D = [0,1]\times[0,1]$, $f \equiv0$, -$c=d=10$, and discretized (\ref{bratu}) using the usual second-order -centered differences over a $100\times100$ mesh of equally -spaced points in $D$. In \gmres($m$), we took $m=10$ and used fast -Poisson right preconditioning as in the experiments in \S2. The computing -environment was as described in \S2. All computing was done -in double precision. - - - -\begin{figure}[ht] -\vspace{2.5in} -\caption{{\rm Log}$_{10}$ of the residual norm versus the number of -{\rm GMRES$(m)$} iterations for the finite difference methods.} -\label{diff} -\end{figure} - - - -In the first set of experiments, we allowed each method to -run for $40$ {\gmresm} iterations, starting with zero as the initial -approximate solution, after which the limit of residual norm -reduction had been reached. The results are shown in Fig.~\ref{diff}. -In Fig.~\ref{diff}, the top curve was produced by method FD1. -The second curve from the top is actually a superposition of -the curves produced by methods EHA2 and FD2; the two curves are -visually indistinguishable. Similarly, the third curve from -the top is a superposition of the curves produced by methods EHA4 -and FD4, and the fourth curve from the top, which lies barely above -the bottom curve, is a superposition of the curves produced by -methods EHA6 and FD6. The bottom curve was produced by method A. - -In the second set of experiments, our purpose was to assess the -relative amount of computational work required by the methods -which use higher-order differencing to reach comparable levels -of residual norm reduction. We compared pairs of methods EHA2 -and FD2, EHA4 and FD4, and EHA6 and FD6 by observing in each of -20 trials the number of {\gmresm} iterations, number of $F$-evaluations, -and run time required by each method to reduce the residual norm -by a factor of $\e$, where for each pair of methods $\e$ was chosen -to be somewhat greater than the limiting ratio of final to -initial residual norms obtainable by the methods. In these trials, -the initial approximate solutions were obtained by generating random -components as in the similar experiments in \S2. We note that for every -method, the numbers of {\gmresm} iterations and $F$-evaluations required -before termination did not vary at all over the 20 trials. The {\gmresm} -iteration counts, numbers of $F$-evaluations, and means and standard -deviations of the run times are given in Table \ref{diffstats}. - -\begin{table} -\caption{Statistics over $20$ trials of {\rm GMRES$(m)$} iteration numbers, -$F$-evaluations, and run times required to reduce the residual norm by -a factor of $\e$. For each method, the number of {\rm GMRES$(m)$} iterations -and $F$-evaluations was the same in every trial.} - -\begin{center} \footnotesize -\begin{tabular}{|c|c|c|c|c|c|} \hline -&& Number of & Number of & Mean Run Time & Standard \\ -Method & $\e$ & Iterations & $F$-Evaluations& (Seconds) & Deviation \\ \hline -\lower.3ex\hbox{EHA2} & \lower.3ex\hbox{$10^{-10}$} & \lower.3ex\hbox{26} & -\lower.3ex\hbox{32} & \lower.3ex\hbox{47.12} & \lower.3ex\hbox{.1048} \\ -FD2 & $10^{-10}$ & 26 & 58 & 53.79 & .1829 \\ \hline -\lower.3ex\hbox{EHA4} & \lower.3ex\hbox{$10^{-12}$} & \lower.3ex\hbox{30} & -\lower.3ex\hbox{42} & \lower.3ex\hbox{56.76} & \lower.3ex\hbox{.1855} \\ -FD4 & $10^{-12}$ & 30 & 132 & 81.35 & .3730 \\ \hline -\lower.3ex\hbox{EHA6} & \lower.3ex\hbox{$10^{-12}$} & \lower.3ex\hbox{30} & -\lower.3ex\hbox{48} & \lower.3ex\hbox{58.56} & \lower.3ex\hbox{.1952} \\ -FD6 & $10^{-12}$ & 30 & 198 & 100.6 & .3278 \\ \hline -\end{tabular} -\end{center} -\label{diffstats} -\end{table} - -In our first set of experiments, we took $c=d=10$ and used right -preconditioning with a fast Poisson solver from {\fishpack} -\cite{Swarztrauber-Sweet}, which is very effective for these -fairly small values of $c$ and $d$. We first started each method -with zero as the initial approximate solution and allowed it -to run for 40 {\gmresm} iterations, after which the limit of residual -norm reduction had been reached. Figure \ref{pdep} shows plots -of the logarithm of the Euclidean norm of the residual versus -the number of {\gmresm} iterations for the three methods. We note -that in Fig.~\ref{pdep} and in all other figures below, the plotted -residual norms were not the values maintained by {\gmresm}, but rather -were computed as accurately as possible ``from scratch.'' That is, -at each {\gmresm} iteration, the current approximate solution was -formed and its product with the coefficient matrix was subtracted -from the right-hand side, all in double precision. -It was important to compute the residual norms in this way because -the values maintained by {\gmresm} become increasingly untrustworthy -as the limits of residual norm reduction are neared; see \cite{Walker88}. -It is seen in Fig.~\ref{pdep} that Algorithm EHA achieved -the same ultimate level of residual norm reduction as the FDP -method and required only a few more {\gmresm} iterations to do -so. - -\begin{figure}[t] -\vspace{3in} -\caption{{\rm Log}$_{10}$ of the residual norm versus the number of -{\rm GMRES}$(m)$ iterations for $c=d=10$ with fast Poisson -preconditioning. Solid curve: Algorithm {\rm EHA}; dotted -curve: {\rm FDP} method; dashed curve: {\rm FSP} method.} -\label{pdep} -\end{figure} - - -In our second set of experiments, we took $c=d=100$ and carried out -trials analogous to those in the first set above. No preconditioning -was used in these experiments, both because we wanted to compare -the methods without preconditioning and because the fast -Poisson preconditioning used in the first set of experiments is -not cost effective for these large values of $c$ and $d$. We first -allowed each method to run for 600 {\gmresm} iterations, -starting with zero as the initial approximate solution, after which -the limit of residual norm reduction had been reached. - - -\section*{Acknowledgments} -The author thanks the anonymous authors whose work largely -constitutes this sample file. He also thanks the INFO-TeX mailing -list for the valuable indirect assistance he received. - - -\begin{thebibliography}{10} -\bibitem{bs} {\sc R.~A. Brualdi and B.~L. Shader}, -{\em On sign-nonsingular matrices and the conversion of the -permanent into the determinant}, in Applied Geometry and -Discrete Mathematics, The Victor Klee Festschrift, P. -Gritzmann and B. Sturmfels, eds., American Mathematical -Society, Providence, RI, 1991, pp. 117--134. - -\bibitem{djd} {\sc J. Drew, C.~R. Johnson, and P. van den Driessche}, -{\em Strong forms of nonsingularity}, Linear Algebra Appl., -162 (1992), to appear. - -\bibitem{g} {\sc P.~M. Gibson}, {\em Conversion of the permanent into the -determinant}, Proc. Amer. Math. Soc., 27 (1971), -pp.~471--476. - -\bibitem{klm} -{\sc V.~Klee, R.~Ladner, and R.~Manber}, {\it -Signsolvability revisited}, Linear Algebra Appl., 59 -(1984), pp.~131--157. - -\bibitem{m} -{\sc K. Murota}, LU-{\em decomposition of a matrix with -entries of different kinds}, Linear Algebra Appl., 49 -(1983), pp.~275--283. - -\bibitem{Axelsson} -{\sc O.~Axelsson}, {\em Conjugate gradient type methods for unsymmetric and - inconsistent systems of linear equations}, Linear Algebra Appl., 29 (1980), - pp.~1--16. - -\bibitem{Brown-Saad1} -{\sc P.~N. Brown and Y.~Saad}, {\em Hybrid {K}rylov methods for nonlinear - systems of equations}, SIAM J. Sci. Statist. Comput., 11 (1990), - pp.~450--481. - -\bibitem{DES} -{\sc R.~S. Dembo, S.~C. Eisenstat, and T.~Steihaug}, {\em Inexact {N}ewton - methods}, SIAM J. Numer. Anal., 19 (1982), pp.~400--408. - -\bibitem{EES} -{\sc S.~C. Eisenstat, H.~C. Elman, and M.~H. Schultz}, {\em Variational - iterative methods for nonsymmetric systems of linear equations}, SIAM J. - Numer. Anal., 20 (1983), pp.~345--357. - -\bibitem{Elman} -{\sc H.~C. Elman}, {\em Iterative methods for large, sparse, nonsymmetric - systems of linear equations}, Ph.D. thesis, Department of Computer - Science, Yale University, New Haven, CT, 1982. - -\bibitem{GloKR85} -{\sc R.~Glowinski, H.~B. Keller, and L.~Rheinhart}, {\em Continuation-conjugate - gradient methods for the least-squares solution of nonlinear boundary value - problems}, SIAM J. Sci. Statist. Comput., 6 (1985), pp.~793--832. - -\bibitem{Golub-VanLoan} -{\sc G.~H. Golub and C.~F. Van~Loan}, {\em Matrix Computations}, - Second ed., The Johns Hopkins University Press, Baltimore, MD, 1989. - -\bibitem{More} -{\sc J.~J. Mor\'e}, {\em A collection of nonlinear model problems}, in - Computational Solutions of Nonlinear Systems of Equations, E.~L. Allgower and - K.~Georg, eds., Lectures in Applied Mathematics, Vol. 26, American - Mathematical Society, Providence, RI, 1990, pp.~723--762. - -\bibitem{Saad} -{\sc Y.~Saad}, {\em Krylov subspace methods for solving large unsymmetric - linear systems}, Math. Comp., 37 (1981), pp.~105--126. - -\bibitem{Saad-Schultz} -{\sc Y.~Saad and M.~H. Schultz}, {\em {\rm GMRES}: A generalized minimal - residual method for solving nonsymmetric linear systems}, SIAM J. Sci. Statist. - Comput., 7 (1986), pp.~856--869. - -\bibitem{Swarztrauber-Sweet} -{\sc P.~N. Swarztrauber and R.~A. Sweet}, {\em Efficient {\rm FORTRAN} - subprograms for the solution of elliptic partial differential equations}, ACM - Trans. Math. Software, 5 (1979), pp.~352--364. - -\bibitem{Walker88} -{\sc H.~F. Walker}, {\em Implementation of the {\rm GMRES} method using - {H}ouseholder transformations}, SIAM J. Sci. Statist. Comput., 9 (1988), - pp.~152--163. - -\bibitem{Walker89} -\sameauthor, {\em Implementations of - the {\rm GMRES} method}, Computer Phys. Comm., 53 (1989), pp.~311--320. - -\end{thebibliography} - -\end{document} - diff --git a/Master/texmf-dist/source/latex/siam/ltexconf.all b/Master/texmf-dist/source/latex/siam/ltexconf.all deleted file mode 100644 index 2e4a638f423..00000000000 --- a/Master/texmf-dist/source/latex/siam/ltexconf.all +++ /dev/null @@ -1,112 +0,0 @@ - -Please answer the following: - -1. Name of conference - -2. Type of Presentation - Contributed: Lecture form - Poster form - Minisymposium: - -3. Equipment for Visual Support - Lecture Form/Minisymposium: - Overhead Projector - 2" x 2" Slide Projector (35mm) - Poster Form: - Easel Poster Board - Other (specify) - -More sophisticated equipment can be provided, but you may be -required to pay the rental fee. For details, indicate your -requirements below: - - -4. If you are a speaker in a minisymposium, who is the organizer? - -5. What is the minisymposium title? - -6. If more than one author, who will present the paper? - -% This is a macro file for creating a SIAM Conference abstract in -% LaTeX. -% -% If you have any questions regarding these macros contact: -% Lillian Hunt -% SIAM -% 3600 University City Center Center -% Philadelphia, PA 19104-2688 -% USA -% (215) 382-9800 -% e-mail:meetings@siam.org - - -\hsize=25.5pc -\vsize=50pc -\textheight 50pc -\textwidth 25.5pc -\parskip 0pt -\parindent 0pt -\pagestyle{plain} - -\def\title#1{\bf{#1}\vspace{6pt}} -\def\abstract#1{\rm {#1}\vspace{6pt}} -\def\author#1{\rm {#1}\vfill\eject} - -% end of style file - -% This is ltexconf.tex. Use this file as an example file for doing an SIAM -% Conference abstract in LaTeX. - - -\documentstyle[ltexconf]{report} -\begin{document} - -\title{Numerical Analysis of a 1-Dimensional -Immersed-Boundary\\ Method} - -\abstract{We present the numerical analysis of a simplified, -one-dimensional version -of Peskin's immersed boundary method, which has been used to -solve -the two- and three-dimensional Navier-Stokes equations in the -presence of immersed boundaries. We consider the heat -equation - in a finite domain with a moving source term. -We denote the solution as $u(x,t)$ and the location of the -source - term as $X(t)$. The source term is a moving delta function -whose strength is a function of u at the location of the -delta function. -The p.d.e. is coupled to an ordinary differential equation -whose -solution gives the location of the source term. - The o.d.e. is $X'(t) = u(X(t),t)$, which can be interpreted as -saying the source term moves at the local velocity. -The accuracy the numerical method of solution depends on how -the -delta function is discretized when the delta function is not -at -a grid point and on how the solution, u, is represented - at locations between grid points. We present results showing -the effect of different choices of spreading the source to -the grid and -of restricting the solution to the source location. -The problem we analyze is also similar to the Stefan problem -and -the immersed-boundary method has features in common with -particle-in-cell - methods.} - \author{\underbar{Richard P. Beyer, Jr.}\\ -University of Washington, Seattle, WA\\ -Randall J. LeVeque\\ -University of Washington, Seattle, WA} - -\end{document} - -% end of example file. - - - -Please furnish complete addresses all co-authors. - -PLEASE INDICATE WHAT CONFERENCE ABSTRACT IS FOR. diff --git a/Master/texmf-dist/source/latex/siam/ltexnec.all b/Master/texmf-dist/source/latex/siam/ltexnec.all deleted file mode 100644 index 9b22936a18c..00000000000 --- a/Master/texmf-dist/source/latex/siam/ltexnec.all +++ /dev/null @@ -1,1923 +0,0 @@ - -This file (ltexnec.all) constitutes the full distribution for NEC Proceedings -Series LaTeX version macros. The files included here are: - -ltexnec.tex (An example file, also containing documentation) - -ltexnec.sty (The style file) - -siamproc.bst (for BiBTeX users) - -To use these macros, separate the files at the indicated cut lines. - -%%%%%%%%%%%%%%%%%%%%%%%%CUT HERE%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - - -% This is ltexnec.tex, an example file for use with the NEC -% Proceedings Series macros. -% Please take the time to read the following comments, as they describe -% how to use these macros. This file can be composed and printed out for -% use as sample output. - -% Any comments or questions regarding these macros should be directed to: -% -% Corey Gray -% SIAM -% 3600 University City Science Center -% Philadelphia, PA 19104-2688 -% USA -% Telephone: (215) 382-9800 -% Fax: (215) 386-7999 -% e-mail: gray@siam.org - - -% This file is to be used as an example for style only. It should not be read -% for content. - -%%%%%%%%%%%%%%% PLEASE NOTE THE FOLLOWING STYLE RESTRICTIONS %%%%%%%%%%%%%%% - -%% 1. There are no new tags. Existing LaTeX tags have been formatted to -%% match the Proceedings series style. -%% -%% 2. You must use \cite in the text to mark your reference citations and -%% \bibitem in the listing of references at the end of your chapter. See -%% the examples in the following file. The file siam.bst has been -%% included for use with BiBTeX. Please be sure to include the appropriate -%% .bib file with BiBTeX submissions. You may also submit the .bbl file -%% instead of the .bib file. -%% -%% 3. Unless otherwise stated by your editor, do your chapter as if it -%% is Chapter 1. The appropriate chapter number will be included during -%% the production of the proceedings. -%% -%% 4. This macro is set up for three levels of headings (\section, -%% \subsection, and \subsubsection). The macro will automatically number -%% the headings for you. -%% -%% 5. The running heads are indicated by the \markboth command. Please -%% define the running heads by placing the authors last names in the -%% first field and the title of the paper in the second field. -%% They should be typed initial cap and lower case. Please see the example. -%% Neither field can contain more than 50 characters including spaces, -%% so please use a shortened version of the title if necessary. For -%% papers with multiple authors please follow these rules; for -%% two authors type {Author 1 and Author 2}; for more that two authors type -%% {Author 1 et al.}. -%% -%% 6. Theorems, Lemmas, Definitions, etc. are to be double-numbered, -%% indicating the section and the occurrence of that element -%% within that section. (For example, the first theorem in the second -%% section would be numbered 2.1. The macro will -%% automatically do the numbering for you. -%% -%% 7. Proofs are handled with the commands \begin{proof}\end{proof}. -%% If you wish to use an end of proof box, use \qed preceding \end{proof}. -%% The example uses one. It is not required. -%% -%% 8. Figures, equations, and tables must be single-numbered. All equation -%% numbers are to be on the left. Figure captions should be placed under -%% the figures they pertain to. Table captions should be placed above -%% the tables. Use existing LaTeX tags for these elements. Numbering of -%% these elements will be done automatically. SIAM supports the use of -%% psfig for including Postscript figures. All Postscript figures should be -%% sent as separate files. A hardcopy version of all Postscript figures -%% is also required. See note regarding this under How to Submit Your Paper. -%% -%% 9. Grant information and author affiliations. -%% This information is included in the file with the two commands, -%% \thanks and \footnotemark []. (See example). The \thanks command -%% produces a footnote for the title or author, and places the -%% appropriate footnote symbol with the title or author and at the -%% bottom of the page. The \footnotemark [] command allows the use of -%% duplicate footnote symbols. This macro follows the normal LaTeX order -%% of footnote symbols. Below is a list of these symbols, and their -%% corresponding footnotemark: -%% -%% asterisk \footnotemark[1] -%% single-dagger \footnotemark[2] -%% double-dagger \footnotemark[3] -%% section sign \footnotemark[4] -%% paragraph \footnotemark[5] -%% parallel \footnotemark[6] -%% double asterisk \footnotemark[7] -%% double single-dagger \footnotemark[8] -%% double double-dagger \footnotemark[9] -%% -%% The following general rules for grants and affiliations apply: -%% a) If there is a single grant for the paper, then the grant -%% information should be footnoted to the title. -%% b) If there is more than one grant, include the grant information -%% with each author's affiliation. -%% c) If there are different grants for the paper but the authors share -%% the same affiliation, footnote the grant information to the title. -%% For example, The work of the first author was supported by xyz. -%% The work of the second author was supported by abc. And so on. -%% d) For authors sharing the same affiliation, use \thanks for the -%% first author with that affiliation and the appropriate -%% \footnotemark[] (from the list above) for all subsequent authors -%% with that affiliation. -%% -%% 10. Special fonts. -%% SIAM supports the use of AMS-TeX fonts version 2.0 and later. As -%% described in the manual for these fonts, they can be included by -%% \input{amssym.def} and \input{amssym.tex}. These macros are not yet -%% updated to make use of the New Font Selection Scheme (NFSS) of -%% Mittelbach and Schopf. To make these macros compatible with NFSS, use -%% the oldlfont style option. -%% -%% 11. How to Submit Your Paper. -%% The electronic version of your paper should be sent to proceed@siam.org. -%% A hardcopy version must also be submitted. Instructions are included -%% in your acceptance letter. Please be sure to send hardcopy -%% versions of any Postscript figures you have submitted electronically. -%% Be sure to return your signed Copyright Transfer Agreement. We cannot -%% publish your paper without it. -%% -%% -%% -%% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%- -%%% - - -\documentstyle[leqno,twoside,11pt,ltexnec]{article} %You must set up your - %\documentstyle line like this. - - -\begin{document} -\cleardoublepage -\pagestyle{myheadings} - -\title{Chapter 1\\ -NEC Proceedings Series Macros\\ - for Use With LaTeX\thanks{Any information regarding grants should be placed -here.}} -\author{J. Corey Gray\thanks{Production Manager, Society for Industrial and Applied -Mathematics, Philadelphia, PA.} -\and -Tricia Manning\thanks{Publications Specialist, Society for Industrial and Applied -Mathematics, Philadelphia, PA.} -\and -Vickie Kearn\thanks{Publisher, Society for Industrial and Applied Mathematics, -Philadelphia, PA.}\\ -\and -Nancy Abbott\thanks{Design Supervisor, Society for Industrial and Applied -Mathematics, Philadelphia, PA} -\and -Sue Ciambrano\thanks{Acquisitions Editor, Society for Industrial and Applied -Mathematics, Philadelphia, PA} -\and -Paul Duggan\thanks{Composition Specialist, Society for Industrial and Applied -Mathematics, Philadelphia, PA} -\and -Robbi Anne Albert\thanks{Production Assistant, Society for Industrial and Applied -Mathematics, Philadelphia, PA} -\and -Jean Anderson\thanks{Composition Coordinator, Society for Industrial and Applied -Mathematics, Philadelphia, PA} -} -\date{} -\maketitle -\markboth{Gray et al.}{SIAM Proceedings Series Macros} % See section 5 above - % for explanation. -\pagenumbering{arabic} - -\begin{abstract}An equivalence is shown between realizability of input/output (i/o) operators by -rational control systems and high-order algebraic differential equations for -i/o pairs. This generalizes, to nonlinear systems, the equivalence -between autoregressive representations and finite dimensional linear -realizability. \end{abstract} -\section{Problem Specification}In this paper, we consider the solution of the $N \times -N$ linear -system -\begin{equation} \label{e1.1} -\cos \sin A x = b -\end{equation} -where $A$ is large, sparse, symmetric, and positive definite. We consider -the direct solution of (\ref{e1.1}) by means of general sparse Gaussian -elimination. In such a procedure, we find a permutation matrix $P$, and -compute the decomposition -\[ -P A P^{t} = L D L^{t} -\] -where $L$ is unit lower triangular and $D$ is diagonal. - - -\section{Design Considerations}Several good ordering algorithms (nested dissection and -minimum degree) -are available for computing $P$ \cite{GEORGELIU}, \cite{ROSE72}. -Since our interest here does not -focus directly on the ordering, we assume for convenience that $P=I$, -or that $A$ has been preordered to reflect an appropriate choice of $P$. - -Our purpose here is to examine the nonnumerical complexity of the -sparse elimination algorithm given in \cite{BANKSMITH}. -As was shown there, a general sparse elimination scheme based on the -bordering algorithm requires less storage for pointers and -row/column indices than more traditional implementations of general -sparse elimination. This is accomplished by exploiting the m-tree, -a particular spanning tree for the graph of the filled-in matrix. - -\begin{theorem} The method was extended to three -dimensions. For the standard multigrid -coarsening -(in which, for a given grid, the next coarser grid has $1/8$ -as many points), anisotropic problems require plane -relaxation to -obtain a good smoothing factor.\end{theorem} - -Several good ordering algorithms (nested dissection and minimum degree) -are available for computing $P$ \cite{GEORGELIU}, \cite{ROSE72}. -Since our interest here does not -focus directly on the ordering, we assume for convenience that $P=I$, -or that $A$ has been preordered to reflect an appropriate choice of $P$. - - -\begin{proof} In this paper we consider two methods. The first method -is -basically the method considered with two differences: -first, we perform plane relaxation by a two-dimensional -multigrid method, and second, we use a slightly different -choice of -interpolation operator, which improves performance -for nearly singular problems. In the second method coarsening -is done by successively coarsening in each of the three -independent variables and then ignoring the intermediate -grids; this artifice simplifies coding considerably.\qed -\end{proof} - -Our purpose here is to examine the nonnumerical complexity of the -sparse elimination algorithm given in \cite{BANKSMITH}. -As was shown there, a general sparse elimination scheme based on the -bordering algorithm requires less storage for pointers and -row/column indices than more traditional implementations of general -sparse elimination. This is accomplished by exploiting the m-tree, -a particular spanning tree for the graph of the filled-in matrix. - -\begin{Definition}{\rm We describe the two methods in \S 1.2. In \S\ 1.3. we -discuss -some remaining details.} -\end{Definition} - -\begin{figure} -\vspace*{24pc} -\caption{This is figure 1.} -\end{figure} - -Our purpose here is to examine the nonnumerical complexity of the -sparse elimination algorithm given in \cite{BANKSMITH}. -As was shown there, a general sparse elimination scheme based on the -bordering algorithm requires less storage for pointers and -row/column indices than more traditional implementations of general -sparse elimination. - -\begin{lemma} We discuss first the choice for $I_{k-1}^k$ -which is a generalization. We assume that $G^{k-1}$ is -obtained -from $G^k$ -by standard coarsening; that is, if $G^k$ is a tensor product -grid $G_{x}^k \times G_{y}^k \times G_{z}^k$, -$G^{k-1}=G_{x}^{k-1} \times G_{y}^{k-1} \times G_{z}^{k-1}$, -where $G_{x}^{k-1}$ is obtained by deleting every other grid -point of $G_x^k$ and similarly for $G_{y}^k$ and $G_{z}^k$. -\end{lemma} - -This is accomplished by exploiting the m-tree, -a particular spanning tree for the graph of the filled-in matrix. -To our knowledge, the m-tree previously has not been applied in this -fashion to the numerical factorization, but it has been used, -directly or indirectly, in several optimal order algorithms for -computing the fill-in during the symbolic factorization phase -\cite{EISENSTAT} - \cite{LIU2}, \cite{ROSE76}, \cite{SCHREIBER}. - -\subsection{Robustness} -We do not -attempt to present an overview -here, but rather attempt to focus on those results that -are relevant to our particular algorithm. -This section assumes prior knowledge of the role of graph theory -in sparse Gaussian elimination; surveys of this role are -available in \cite{ROSE72} and \cite{GEORGELIU}. More general -discussions of elimination trees are given in -\cite{LAW} - \cite{LIU2}, \cite{SCHREIBER}. -Thus, at the $k$th stage, the bordering algorithm consists of -solving the lower triangular system -\begin{equation} \label{1.2} - L_{k-1}v = c -\end{equation} -and setting -\begin{eqnarray} -\ell &=& D^{-1}_{k-1}v , \\ -\delta &=& \alpha - \ell^{t} v . -\end{eqnarray} - -\subsubsection{Versatility.} We do not -attempt to present an overview -here, but rather attempt to focus on those results that -are relevant to our particular algorithm. - -\section{Conclusions} The special -structure of this problem allows us to make exact estimates of -the complexity. For the old approach, we show that the -complexity of the intersection problem is $O(n^{3})$, the same -as the complexity of the numerical computations -\cite{GEORGELIU}, \cite{ROSEWHITTEN}. For the -new approach, the complexity of the second part is reduced to -$O(n^{2} (\log n)^{2})$. - -\begin{thebibliography}{99} - - -\bibitem{BANKSMITH} -R.~E. Bank and R.~K. Smith, {\em General sparse elimination requires no - permanent integer storage}, SIAM J. Sci. Stat. Comput., 8 (1987), - pp.~574--584. - -\bibitem{EISENSTAT} -S.~C. Eisenstat, M.~C. Gursky, M.~Schultz, and A.~Sherman, {\em - Algorithms and data structures for sparse symmetric gaussian elimination}, - SIAM J. Sci. Stat. Comput., 2 (1982), pp.~225--237. - -\bibitem{GEORGELIU} -A.~George and J.~Liu, {\em Computer Solution of Large Sparse Positive - Definite Systems}, Prentice Hall, Englewood Cliffs, NJ, 1981. - -\bibitem{LAW} -K.~H. Law and S.~J. Fenves, {\em A node addition model for symbolic - factorization}, ACM TOMS, 12 (1986), pp.~37--50. - -\bibitem{LIU} -J.~W.~H. Liu, {\em A compact row storage scheme for cholesky factors - using elimination trees}, ACM TOMS, 12 (1986), pp.~127--148. - -\bibitem{LIU2} -\sameauthor , {\em The role of - elimination trees in sparse factorization}, Tech. Report CS-87-12,Department - of Computer Science, York University, Ontario, Canada, 1987. - -\bibitem{ROSE72} -D.~J. Rose, {\em A graph theoretic study of the numeric solution of - sparse positive definite systems}, in Graph Theory and Computing, AcademicΠPress, New -York, 1972. - -\bibitem{ROSE76} -D.~J. Rose, R.~E. Tarjan, and G.~S. Lueker, {\em Algorithmic aspects of - vertex elimination on graphs}, SIAM J. Comput., 5 (1976), pp.~226--283. - -\bibitem{ROSEWHITTEN} -D.~J. Rose and G.~F. Whitten, {\em A recursive analysis of disection - strategies}, in Sparse Matrix Computations, Academic Press, New York, 1976. - -\bibitem{SCHREIBER} -R.~Schrieber, {\em A new implementation of sparse gaussian elimination}, - ACM TOMS, 8 (1982), pp.~256--276. - -\end{thebibliography} - -\end{document} - - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%CUT HERE%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -% -% -% This file may be freely distributed but may not be altered in any way. -% Any comments or questions regarding these macros should be directed to: - -% Corey Gray -% SIAM -% 3600 University City Science Center -% Philadelphia, PA 19104-2688 -% USA -% Telephone: (215) 382-9800 -% Fax: (215) 386-7999 -% e-mail: gray@siam.org - -% This is a file of macros and definitions for creating a chapter for -% publication in the NEC Proceedings series using LaTeX. - -% Report the version. -\message{*** NEC LaTeX Proceedings Series macro package, version 1.0, -July 10, 1992 ***} -%\input proceed.sty - -\pretolerance=800 -\tolerance=10000 -\sloppy - - -\vsize=49pc -\hsize=30pc -\baselineskip=13pt -\hoffset -.5in -\voffset -.5in -\footskip=18pt -\topmargin 24pt -\headheight 12pt -\headsep 17pt -\textheight 49pc \advance\textheight by \topskip -\textwidth 30pc -\parskip 0pt -\parindent 18pt -\def\topfraction{.9} -\def\textfraction{.1} -\def\topnumber{2} -%% footnotes to be set 8/10 -\def\footnotesize{\@setsize\footnotesize{11pt}\ixpt\@ixpt - % \indent - \abovedisplayskip \z@ - \belowdisplayskip\z@ - \abovedisplayshortskip\abovedisplayskip - \belowdisplayshortskip\belowdisplayshortskip -\def\@listi{\leftmargin\leftmargini \topsep 3pt plus 1pt minus 1pt - \parsep 2pt plus 1pt minus 1pt - \itemsep \parsep}} - -\let\referencesize\footnotesize - -\footnotesep 0pt - -\skip\footins 12pt plus 12pt - -\def\footnoterule{\kern3\p@ \hrule width 3em\vspace{3pt}} % the \hrule is -%.4pt high - - -\def\ps@plain{\let\@mkboth\@gobbletwo - \def\@oddfoot{{\hfil\small\thepage\hfil}}% - \def\@evenfoot{{\hfil\small\thepage\hfil}}% -\def\@oddhead{} - \def\@evenhead{}%\def\@evenfoot{} -} - - - -\def\ps@headings{\let\@mkboth\markboth - \def\@oddfoot{}\def\@evenfoot{}% - \def\@evenhead{{\rm\thepage}\hspace*{2pc}{\small\leftmark}\hfil}% - -\def\@oddhead{\hfil{\noindent\small\rightmark}\hspace*{2pc}{\rm\thepage}}% - -% \def\chaptermark##1{\markboth{\uppercase{% - % {\protect\small\@chapapp}\ -%{\protect\small\thechapter}}}% - % {\uppercase{##1}}}% - } - - -\def\ps@myheadings{\let\@mkboth\@gobbletwo - \def\@oddfoot{}\def\@evenfoot{}% - -\def\@oddhead{\hfil{\small\rightmark}\hspace*{2pc}{\normalsize\rm\thepage}} -% - -\def\@evenhead{{\normalsize\rm\thepage}\hspace*{2pc}{\small\leftmark}\hfil} -% -% \def\chaptermark##1{}% - % \def\sectionmark##1{}\def\subsectionmark##1{}} -} - - - -\def\theequation{\arabic{equation}} -%\def\theequation{\arabic{chapter}.\arabic{equation}} - -\def\abstract{\if@twocolumn -\section*{Abstract} -\else \small -\begin{center} -{\bf Abstract\vspace{-.5em}\vspace{3pt}} -\end{center} -\quotation -\fi} -\def\endabstract{\if@twocolumn\else\endquotation\fi} - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% % -% THEOREMS, PROOFS, ALGORITHMS % -% % -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -%%% defined proof environment by theorem model (took out counter) - -\def\newproof#1{\@nprf{#1}} - -\def\@nprf#1#2{\@xnprf{#1}{#2}} - -\def\@xnprf#1#2{\expandafter\@ifdefinable\csname #1\endcsname -\global\@namedef{#1}{\@prf{#1}{#2}}\global\@namedef{end#1}{\@endproof}} - -\def\@prf#1#2{\@xprf{#1}{#2}} - -\def\@xprf#1#2{\@beginproof{#2}{\csname the#1\endcsname}\ignorespaces} - - - -%%% defined algorithm environment by theorem model - -\def\newalgorithm#1{\@ifnextchar[{\@oalg{#1}}{\@nalg{#1}}} - -\def\@nalg#1#2{% -\@ifnextchar[{\@xnalg{#1}{#2}}{\@ynalg{#1}{#2}}} - -\def\@xnalg#1#2[#3]{\expandafter\@ifdefinable\csname #1\endcsname -{\@definecounter{#1}\@addtoreset{#1}{#3}% -\expandafter\xdef\csname the#1\endcsname{\expandafter\noexpand - \csname the#3\endcsname \@thmcountersep \@thmcounter{#1}}% -\global\@namedef{#1}{\@alg{#1}{#2}}\global\@namedef{end#1}{\@endalgorithm}} -} - -\def\@ynalg#1#2{\expandafter\@ifdefinable\csname #1\endcsname -{\@definecounter{#1}% -\expandafter\xdef\csname the#1\endcsname{\@thmcounter{#1}}% -\global\@namedef{#1}{\@alg{#1}{#2}}\global\@namedef{end#1}{\@endalgorithm}} -} - -\def\@oalg#1[#2]#3{\expandafter\@ifdefinable\csname #1\endcsname - {\global\@namedef{the#1}{\@nameuse{the#2}}% -\global\@namedef{#1}{\@alg{#2}{#3}}% -\global\@namedef{end#1}{\@endalgorithm}}} - -\def\@alg#1#2{\refstepcounter - {#1}\@ifnextchar[{\@yalg{#1}{#2}}{\@xalg{#1}{#2}}} - -\def\@xalg#1#2{\@beginalgorithm{#2}{\csname the#1\endcsname}\ignorespaces} -\def\@yalg#1#2[#3]{\@opargbeginalgorithm{#2}{\csname - the#1\endcsname}{#3}\ignorespaces} - - - - -\def\@beginproof#1{\rm {\it #1.\ }} -\def\@endproof{\outerparskip 0pt\endtrivlist} - -\def\@begintheorem#1#2{\it {\sc #1\ #2.\ }} -\def\@opargbegintheorem#1#2#3{\it - {\sc #1\ #2\ (#3).\ }} -\def\@endtheorem{\outerparskip 0pt\endtrivlist} - -%\def\@begindefinition#1#2{\rm \trivlist \item[\hskip \labelsep{\sc #1\#2.}]} -%\def\@opargbegindefinition#1#2#3{\rm \trivlist -% \item[\hskip \labelsep{\sc #1\ #2.\ (#3)}]} -%\def\@enddefinition{\outerparskip 0pt\endtrivlist} - - -\def\@beginalgorithm#1#2{\rm \trivlist \item[\hskip \labelsep{\sc #1\#2.}]} -\def\@opargbeginalgorithm#1#2#3{\rm \trivlist - \item[\hskip \labelsep{\sc #1\ #2.\ (#3)}]} -\def\@endalgorithm{\outerparskip 6pt\endtrivlist} - - -\newskip\outerparskip - -\def\trivlist{\parsep\outerparskip - \@trivlist \labelwidth\z@ \leftmargin\z@ - \itemindent\parindent \def\makelabel##1{##1}} - -\def\@trivlist{\topsep=0pt\@topsepadd\topsep - \if@noskipsec \leavevmode \fi - \ifvmode \advance\@topsepadd\partopsep \else \unskip\par\fi - \if@inlabel \@noparitemtrue \@noparlisttrue - \else \@noparlistfalse \@topsep\@topsepadd \fi - \advance\@topsep \parskip - \leftskip\z@\rightskip\@rightskip \parfillskip\@flushglue - \@setpar{\if@newlist\else{\@@par}\fi}% - \global\@newlisttrue \@outerparskip\parskip} - - -\def\endtrivlist{\if@newlist\@noitemerr\fi - \if@inlabel\indent\fi - \ifhmode\unskip \par\fi - \if@noparlist \else - \ifdim\lastskip >\z@ \@tempskipa\lastskip \vskip -\lastskip - \advance\@tempskipa\parskip \advance\@tempskipa -\@outerparskip - \vskip\@tempskipa - \fi\@endparenv\fi - \vskip\outerparskip} - - - - \newproof{@proof}{Proof} - \newenvironment{proof}{\begin{@proof}}{\end{@proof}} - - \newtheorem{@theorem}{Theorem}[section] - \newenvironment{theorem}{\begin{@theorem}}{\end{@theorem}} - -% \newalgorithm{@algorithm}{Algorithm}[section] -% \newenvironment{algorithm}{\begin{@algorithm}}{\end{@algorithm}} - - - -\newtheorem{lemma}{Lemma}[section] -\newtheorem{fact}{Fact}[section] -\newtheorem{corollary}{Corollary}[section] -\newtheorem{axiom}{Axiom}[section] -\newtheorem{cond}{Condition}[section] -\newtheorem{property}{Property}[section] -\newtheorem{proposition}{Proposition}[section] - -\newtheorem{Conjecture}{Conjecture}[section] -\newtheorem{Corollary}{Corollary}[section] -\newtheorem{Definition}{Definition}[section] -\newtheorem{Lemma}{Lemma}[section] -\newtheorem{Remark}{Remark}[section] - -\newproof{Example}{Example} -\newproof{Method}{Method} -\newproof{Exercise}{Exercise} - -\def\qed{{\qquad \vbox{\hrule\hbox{% - \vrule height1.3ex\hskip0.8ex\vrule}\hrule - }}\par} -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% % -% TABLE AND FIGURE CAPTIONS % -% % -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - \def\@figtxt{figure} -\long\def\@makecaption#1#2{\small -\setlength{\parindent}{18pt} -\baselineskip 14pt - \ifx\@captype\@figtxt - \vskip 10pt - \setbox\@tempboxa\hbox{{\sc #1} {\it #2}} - \ifdim \wd\@tempboxa >\hsize {\sc #1} {\it #2}\par \else \hbox -to\hsize{\hfil\box\@tempboxa\hfil}% - \fi\else\hbox to\hsize{\hfil{\sc #1}\hfil}% - \setbox\@tempboxa\hbox{{\it #2}}% - \ifdim \wd\@tempboxa >\hsize {\it #2}\par \else - \hbox to \hsize{\hfil\box\@tempboxa\hfil}\fi - \vskip 10pt - \fi} - - -%\newif\iftable \global\tablefalse - - -%\long\def\@makecaption#1#2{% -%\setlength{\parindent}{18pt} -% \vskip 12pt -% \iftable - % \hbox to \hsize{\hfil\sc #1\hfil} - % \hbox to \hsize{\hfil\it #2\hfil} - % \global\tablefalse - % \else - % \setbox\@tempboxa\hbox{{\small#1} {\small\it#2}} - % \ifdim \wd\@tempboxa >\hsize - % \indent{\small#1}{\small\it#2}\par - % \else - % \hbox to\hsize{\hfil\box\@tempboxa\hfil}\fi - % \fi} -% \vskip 6pt} - - - -%\def\figure{\global\tablefalse\@float{figure}} -\def\fnum@figure{\par\sc Fig. \thefigure.\ } -%\def\fnum@figure{\par\sc Fig. \thefigure\ } - -%\def\table{\global\tabletrue\@float{table}} -\def\fnum@table{\small \sc Table \thetable} - - - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% % -% CHAPTER % -% % -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -%\def\@chapapp{Chapter} - -%\def\@makechapterhead#1{% - % \vspace*{8pt} - % \vtop to 11pc{\leftskip=0pc \parindent 0pt - % \begin{center}{\large \@chapapp}%\end{flushright}%%% - % {\large \baselineskip=26pt\ \thechapter}\end{center}\vskip-8pt -% \vrule width 31pc height .5pt\par % - % \vspace*{6pt}% - % \baselineskip=18pt\begin{center}{\Large#1 }\end{center}\par - % \vfil}} - -%\def\@makeschapterhead#1{% - % \vspace*{8pt} - % \vtop to 11pc{\leftskip=0pc \parindent 0pt - % \vtop to 26pt{\vfill}\vskip-8pt - % \vrule width 31pc height .5pt\par % -% % \vspace*{6pt}% - % {\Large #1}\par - % \vfil}} - - -%\def\chapter{\cleardoublepage \thispagestyle{plain} \global\@topnum\z@ - % \@afterindentfalse \secdef\@chapter\@schapter} - -%\def\author#1{\vspace*{-6.25pc}\begin{center}{#1}\end{center} - % \par\vspace*{4pc}} -%\def\chaptermark#1{} - -%\def\@chapter[#1]#2{% - % \refstepcounter{chapter} - % \typeout{Chapter\space\thechapter.} -% % \addcontentsline{toc}{chapter}{CHAPTER\ \thechapter. #1} - % \protect\addtocontents{lof}{\protect\addvspace{10pt}} - % \protect\addtocontents{lot}{\protect\addvspace{10pt}} - % \chaptermark{#1} - % \@makechapterhead{#2} - % \@afterheading} - - - -%\def\@schapter#1{\@makeschapterhead{#1} - % \@afterheading} - - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% % -% SECTIONS % -% % -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -\def\section{\@startsection {section}{1}{\z@}{-3.5ex plus -1ex minus - -.2ex}{2.3ex plus .2ex}{\large\bf}} -\def\subsection{\@startsection{subsection}{2}{\z@}{-3.25ex plus -1ex minus - -.2ex}{1.5ex plus .2ex}{\large\bf}} -\def\subsubsection{\@startsection{subsubsection}{3}{\z@}{-3.25ex plus - -1ex minus -.2ex}{1.5ex plus .2ex}{\large\bf}} -%\renewcommand{\section}{\@startsection {section}{1}{\z@}{-3.5ex plus -1ex -%minus -% -.2ex}{2.3ex plus .2ex}{\large\bf}} - -%\def\@sect#1#2#3#4#5#6[#7]#8{\ifnum #2>\c@secnumdepth -% \def\@svsec{}\else -% \refstepcounter{#1}\edef\@svsec{\csname the#1\endcsname.\hskip .75em -%}\fi% -% - % \@tempskipa #5\relax - % \ifdim \@tempskipa>\z@ - % \begingroup #6\relax - % \@hangfrom{\hskip #3\relax\@svsec}{\interlinepenalty \@M #8\par} - % \endgroup -% \csname #1mark\endcsname{#7}\addcontentsline - %{toc}{#1}{\ifnum #2>\c@secnumdepth \else - % \protect\numberline{\csname the#1\endcsname}\fi - % #7}\else - % \def\@svsechd{#6\hskip #3\@svsec #8\hskip1em\csname #1mark\endcsname - - % {#7}\addcontentsline - % {toc}{#1}{\ifnum #2>\c@secnumdepth \else - % \protect\numberline{\csname the#1\endcsname}\fi - % #7}}\fi - % \@xsect{#5}} - - - %\@startsection {NAME}{LEVEL}{INDENT}{BEFORESKIP}{AFTERSKIP}{STYLE} -%\def\section{\@startsection{section}{1}{0pt}{-12pt}{3pt}{\hyphenpenalty=\@ -%M -%\exhyphenpenalty=\@M\normalsize\bf}} -%\def\subsection{\@startsection{subsection}{2}{0pt}{-12pt}{0pt}{\normalsize -%\bf} -%} -%\def\subsubsection{\@startsection -% {subsubsection}{3}{0pt}{-12pt}{0pt}{\normalsize\bf}} -%\def\paragraph{\@startsection -% {paragraph}{4}{\parindent}{0pt}{0pt}{\normalsize\bf}} -%\def\subparagraph{\@startsection -% {subparagraph}{4}{\parindent}{0pt}{0pt}{\normalsize\bf}} -%\def\thepart{\Roman{part}} -%\def\thesection {\arabic{section}.} -%\def\thesubsection {\thesection\arabic{subsection}.} -%\def\thesubsubsection {\thesubsection .\arabic{subsubsection}.} -%\def\theparagraph {\thesubsubsection.\arabic{paragraph}.} -%\def\thesubparagraph {\theparagraph.\arabic{subparagraph}.} - - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% % -% TOC % -% % -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -%% sets chapter in toc -%\def\l@chapter#1#2{\pagebreak[3] -% \hbox to \hsize{\null\hskip2pc -% \llap{\hbox to\@pnumwidth{\hss#2}\hskip2pc}% -% #1\hfill}\vskip1pc} - - -%%% set so only chapters print in TOC -%\def\@dottedtocline#1#2#3#4#5{\relax} - - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% %% -%% BIBLIOGRAPHY %% -%% %% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - - -\def\thebibliography#1{% -%\cleardoublepage -\parindent 0em -\vspace{9pt} -\begin{flushleft}\large\bf {References}\end{flushleft} -\addvspace{3pt}\nopagebreak\list - %% default is no labels, for those not using \cite or BibTeX -{[\arabic{enumi}]} {\settowidth\labelwidth{[#1]} -%%{[\arabic{enumi}]}{\settowidth\labelwidth{mm} -\leftmargin\labelwidth -\leftmargin=12pt - \advance\leftmargin\labelsep - \usecounter{enumi}\@bibsetup} -\def\newblock{\hskip .11em plus .33em minus -.07em} - \sloppy\clubpenalty4000\widowpenalty4000 - \sfcode`\.=1000\relax} - -%\def\thebibliography#1{% -%\cleardoublepage -%\parindent 0em -%\vspace{9pt} -%\begin{flushleft}\Large\bf{References} \end{flushleft} -%\addvspace{3pt}\nopagebreak\list -%% %% default is no labels, for those not using \cite or BibTeX -%%% {[\arabic{enumi}]} {\settowidth\labelwidth{[#1]} -%{[\arabic{enumi}]}{\settowidth\labelwidth{mm} -%%{}{\settowidth\labelwidth{mm} -%\leftmargin\labelwidth -%\advance -%\leftmargin 0pt \itemindent -16pt -% \usecounter{enumi}\@bibsetup} -%\def\newblock{\hskip .11em plus .33em minus -.07em} -% \sloppy\clubpenalty4000\widowpenalty4000 -% \sfcode`\.=1000\relax} - -%% setup 8/10 type -\def\@bibsetup{%\itemindent=0pt -\itemsep=0pt \parsep=0pt -\small} - -\def\sameauthor{\leavevmode\vrule height 2pt depth -1.6pt width 23pt} - - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% % -% INDEX % -% % -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - - -%makeindex.sty official version 6.4 -%The second line came from /usr/misc/lib/tex82/report.sty. - -\def\theindex{\@restonecoltrue\if@twocolumn\@restonecolfalse\fi -\columnseprule \z@ -\columnsep 35pt\twocolumn[\chapter*{Index}] - \parskip\z@ plus .3pt\relax\let\item\@idxitem} - - -\def\printindex{\cleardoublepage\markboth{INDEX}{INDEX} -\addcontentsline{toc}{chapter}{Index}\@input{\jobname.ind}} - -\ps@headings - - -%%% end of original style file - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%CUT HERE%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - - -% SIAM bibliography style (29-Jan-88 version) -% numeric labels, alphabetic order, Mathematical Reviews abbreviations, -% names in \sc, titles in italics, book titles mixed upper-lower and article -% titles lowercase, commas separate all fields except before "notes". -% -% History -% 1/30/86 (HWT) Original version, by Howard Trickey. -% 6/15/87 (HWT) Fix format.editors---Martin Costabel. -% 1/29/88 (OP&HWT) Updated for BibTeX version 0.99a, Oren Patashnik; -% THIS `siam' VERSION DOES NOT WORK WITH BIBTEX 0.98i. - -ENTRY - { address - author - booktitle - chapter - edition - editor - howpublished - institution - journal - key - month - note - number - organization - pages - publisher - school - series - title - type - volume - year - } - {} - { label } - -INTEGERS { output.state before.all mid.sentence after.block } - -FUNCTION {init.state.consts} -{ #0 'before.all := - #1 'mid.sentence := - #2 'after.block := -} - -STRINGS { s t } - -FUNCTION {output.nonnull} -{ 's := - output.state mid.sentence = - { ", " * write$ } - { output.state after.block = - { add.period$ write$ - newline$ - "\newblock " write$ - } - 'write$ - if$ - mid.sentence 'output.state := - } - if$ - s -} - -FUNCTION {output} -{ duplicate$ empty$ - 'pop$ - 'output.nonnull - if$ -} - -FUNCTION {output.check} -{ 't := - duplicate$ empty$ - { pop$ "empty " t * " in " * cite$ * warning$ } - 'output.nonnull - if$ -} - -FUNCTION {output.bibitem} -{ newline$ - "\bibitem{" write$ - cite$ write$ - "}" write$ - newline$ - "" - before.all 'output.state := -} - -FUNCTION {fin.entry} -{ add.period$ - write$ - newline$ -} - -FUNCTION {new.block} -{ output.state before.all = - 'skip$ - { after.block 'output.state := } - if$ -} - -FUNCTION {not} -{ { #0 } - { #1 } - if$ -} - -FUNCTION {and} -{ 'skip$ - { pop$ #0 } - if$ -} - -FUNCTION {or} -{ { pop$ #1 } - 'skip$ - if$ -} - -FUNCTION {new.block.checka} -{ empty$ - 'skip$ - 'new.block - if$ -} - -FUNCTION {field.or.null} -{ duplicate$ empty$ - { pop$ "" } - 'skip$ - if$ -} - -FUNCTION {emphasize} -{ duplicate$ empty$ - { pop$ "" } - { "{\em " swap$ * "}" * } - if$ -} - -FUNCTION {scapify} -{ duplicate$ empty$ - { pop$ "" } - { "{\sc " swap$ * "}" * } - if$ -} - -INTEGERS { nameptr namesleft numnames } - -FUNCTION {format.names} -{ 's := - #1 'nameptr := - s num.names$ 'numnames := - numnames 'namesleft := - { namesleft #0 > } - { s nameptr "{f.~}{vv~}{ll}{, jj}" format.name$ 't := - nameptr #1 > - { namesleft #1 > - { ", " * t * } - { numnames #2 > - { "," * } - 'skip$ - if$ - t "others" = - { " et~al." * } - { " and " * t * } - if$ - } - if$ - } - 't - if$ - nameptr #1 + 'nameptr := - namesleft #1 - 'namesleft := - } - while$ -} - -STRINGS { last.authors } - -FUNCTION {init.last.authors} -{ "" 'last.authors := -} - -FUNCTION {format.authors} -{ author empty$ - { "" 'last.authors := - "" - } - { author last.authors = - { "\leavevmode\vrule height 2pt depth -1.6pt width 23pt" } - { author format.names }% scapify } - if$ - author 'last.authors := - } - if$ -} - -FUNCTION {format.organization} -{ organization empty$ - { "" 'last.authors := - "" - } - { organization last.authors = - { "\leavevmode\vrule height 2pt depth -1.6pt width 23pt" } - { organization scapify } - if$ - organization 'last.authors := - } - if$ -} - -FUNCTION {format.editors} -{ editor empty$ - { "" 'last.authors := - "" - } - { editor last.authors = - { "\leavevmode\vrule height 2pt depth -1.6pt width 23pt" } - { editor format.names scapify } - if$ - editor num.names$ #1 > - { ", eds." * } - { ", ed." * } - if$ - editor 'last.authors := - } - if$ -} - -FUNCTION {format.ineditors} -{ editor empty$ - { "" } - { editor format.names - editor num.names$ #1 > - { ", eds." * } - { ", ed." * } - if$ - } - if$ -} - -FUNCTION {format.title} -{ title empty$ - { "" } - { title "t" change.case$ emphasize } - if$ -} - -FUNCTION {n.dashify} -{ 't := - "" - { t empty$ not } - { t #1 #1 substring$ "-" = - { t #1 #2 substring$ "--" = not - { "--" * - t #2 global.max$ substring$ 't := - } - { { t #1 #1 substring$ "-" = } - { "-" * - t #2 global.max$ substring$ 't := - } - while$ - } - if$ - } - { t #1 #1 substring$ * - t #2 global.max$ substring$ 't := - } - if$ - } - while$ -} - -FUNCTION {format.date} -{ year empty$ - { month empty$ - { "" } - { "there's a month but no year in " cite$ * warning$ - month - } - if$ - } - { month empty$ - 'year - { month " " * year * } - if$ - } - if$ -} - -FUNCTION {format.btitle} -{ title emphasize -} - -FUNCTION {tie.or.space.connect} -{ duplicate$ text.length$ #3 < - { "~" } - { " " } - if$ - swap$ * * -} - -FUNCTION {either.or.check} -{ empty$ - 'pop$ - { "can't use both " swap$ * " fields in " * cite$ * warning$ } - if$ -} - -FUNCTION {format.bvolume} -{ volume empty$ - { "" } - { "vol.~" volume * - series empty$ - 'skip$ - { " of " * series * } - if$ - "volume and number" number either.or.check - } - if$ -} - -FUNCTION {format.number.series} -{ volume empty$ - { number empty$ - { series field.or.null } - { "no.~" number * - series empty$ - { "there's a number but no series in " cite$ * warning$ } - { " in " * series * } - if$ - } - if$ - } - { "" } - if$ -} - -FUNCTION {format.edition} -{ edition empty$ - { "" } - { edition "l" change.case$ "~ed." * } - if$ -} - -INTEGERS { multiresult } - -FUNCTION {multi.page.check} -{ 't := - #0 'multiresult := - { multiresult not - t empty$ not - and - } - { t #1 #1 substring$ - duplicate$ "-" = - swap$ duplicate$ "," = - swap$ "+" = - or or - { #1 'multiresult := } - { t #2 global.max$ substring$ 't := } - if$ - } - while$ - multiresult -} - -FUNCTION {format.pages} -{ pages empty$ - { "" } - { pages multi.page.check - { "pp.~" pages n.dashify * } - { "p.~" pages * } - if$ - } - if$ -} - -FUNCTION {format.vol.year} -{ volume field.or.null - year empty$ - { "empty year in " cite$ * warning$ } - { " (" year * ")" * * } - if$ -} - -FUNCTION {format.chapter.pages} -{ chapter empty$ - 'format.pages - { type empty$ - { "ch.~" chapter * } - { type "l" change.case$ chapter tie.or.space.connect } - if$ - pages empty$ - 'skip$ - { ", " * format.pages * } - if$ - } - if$ -} - -FUNCTION {format.in.ed.booktitle} -{ booktitle empty$ - { "" } - { editor empty$ - { "in " booktitle * } - { "in " booktitle * ", " * format.ineditors * } - if$ - } - if$ -} - -FUNCTION {empty.misc.check} -{ author empty$ title empty$ howpublished empty$ - month empty$ year empty$ note empty$ - and and and and and - key empty$ not and - { "all relevant fields are empty in " cite$ * warning$ } - 'skip$ - if$ -} - -FUNCTION {format.thesis.type} -{ type empty$ - 'skip$ - { pop$ - type "l" change.case$ - } - if$ -} - -FUNCTION {format.tr.number} -{ type empty$ - { "Tech. Rep." } - 'type - if$ - number empty$ - { "l" change.case$ } - { number tie.or.space.connect } - if$ -} - -FUNCTION {format.article.crossref} -{ key empty$ - { journal empty$ - { "need key or journal for " cite$ * " to crossref " * crossref * - warning$ - "" - } - { "in " journal * } - if$ - } - { "in " key * } - if$ - " \cite{" * crossref * "}" * -} - -FUNCTION {format.crossref.editor} -{ editor #1 "{vv~}{ll}" format.name$ - editor num.names$ duplicate$ - #2 > - { pop$ " et~al." * } - { #2 < - 'skip$ - { editor #2 "{ff }{vv }{ll}{ jj}" format.name$ "others" = - { " et~al." * } - { " and " * editor #2 "{vv~}{ll}" format.name$ * } - if$ - } - if$ - } - if$ -} - -FUNCTION {format.book.crossref} -{ volume empty$ - { "empty volume in " cite$ * "'s crossref of " * crossref * warning$ - "in " - } - { "vol.~" volume * - " of " * - } - if$ - editor empty$ - editor field.or.null author field.or.null = - or - { key empty$ - { series empty$ - { "need editor, key, or series for " cite$ * " to crossref " * - crossref * warning$ - "" * - } - { series * } - if$ - } - { key * } - if$ - } - { format.crossref.editor * } - if$ - " \cite{" * crossref * "}" * -} - -FUNCTION {format.incoll.inproc.crossref} -{ editor empty$ - editor field.or.null author field.or.null = - or - { key empty$ - { booktitle empty$ - { "need editor, key, or booktitle for " cite$ * " to crossref " * - crossref * warning$ - "" - } - { "in " booktitle * } - if$ - } - { "in " key * } - if$ - } - { "in " format.crossref.editor * } - if$ - " \cite{" * crossref * "}" * -} - -FUNCTION {article} -{ output.bibitem - format.authors "author" output.check - format.title "title" output.check - crossref missing$ - { journal "journal" output.check - format.vol.year output - } - { format.article.crossref output.nonnull } - if$ - format.pages output - new.block - note output - fin.entry -} - -FUNCTION {book} -{ output.bibitem - author empty$ - { format.editors "author and editor" output.check } - { format.authors output.nonnull - crossref missing$ - { "author and editor" editor either.or.check } - 'skip$ - if$ - } - if$ - format.btitle "title" output.check - crossref missing$ - { format.bvolume output - format.number.series output - publisher "publisher" output.check - address output - } - { format.book.crossref output.nonnull } - if$ - format.edition output - format.date "year" output.check - new.block - note output - fin.entry -} - -FUNCTION {booklet} -{ output.bibitem - format.authors output - format.title "title" output.check - howpublished new.block.checka - howpublished output - address output - format.date output - new.block - note output - fin.entry -} - -FUNCTION {inbook} -{ output.bibitem - author empty$ - { format.editors "author and editor" output.check } - { format.authors output.nonnull - crossref missing$ - { "author and editor" editor either.or.check } - 'skip$ - if$ - } - if$ - format.btitle "title" output.check - crossref missing$ - { format.bvolume output - format.number.series output - publisher "publisher" output.check - address output - } - { format.book.crossref output.nonnull } - if$ - format.edition output - format.date "year" output.check - format.chapter.pages "chapter and pages" output.check - new.block - note output - fin.entry -} - -FUNCTION {incollection} -{ output.bibitem - format.authors "author" output.check - format.title "title" output.check - crossref missing$ - { format.in.ed.booktitle "booktitle" output.check - format.bvolume output - format.number.series output - publisher "publisher" output.check - address output - format.edition output - format.date "year" output.check - } - { format.incoll.inproc.crossref output.nonnull } - if$ - format.chapter.pages output - new.block - note output - fin.entry -} - -FUNCTION {inproceedings} -{ output.bibitem - format.authors "author" output.check - format.title "title" output.check - crossref missing$ - { format.in.ed.booktitle "booktitle" output.check - format.bvolume output - format.number.series output - address empty$ - { organization output - publisher output - format.date "year" output.check - } - { address output.nonnull - format.date "year" output.check - organization output - publisher output - } - if$ - } - { format.incoll.inproc.crossref output.nonnull } - if$ - format.pages output - new.block - note output - fin.entry -} - -FUNCTION {conference} { inproceedings } - -FUNCTION {manual} -{ output.bibitem - author empty$ - { format.organization output } - { format.authors output.nonnull } - if$ - format.btitle "title" output.check - author empty$ - 'skip$ - { organization output } - if$ - address output - format.edition output - format.date output - new.block - note output - fin.entry -} - -FUNCTION {mastersthesis} -{ output.bibitem - format.authors "author" output.check - format.title "title" output.check - "Master's thesis" format.thesis.type output.nonnull - school "school" output.check - address output - format.date "year" output.check - new.block - note output - fin.entry -} - -FUNCTION {misc} -{ output.bibitem - format.authors output - format.title output - howpublished new.block.checka - howpublished output - format.date output - new.block - note output - fin.entry - empty.misc.check -} - -FUNCTION {phdthesis} -{ output.bibitem - format.authors "author" output.check - format.btitle "title" output.check - "PhD thesis" format.thesis.type output.nonnull - school "school" output.check - address output - format.date "year" output.check - new.block - note output - fin.entry -} - -FUNCTION {proceedings} -{ output.bibitem - editor empty$ - { format.organization output } - { format.editors output.nonnull } - if$ - format.btitle "title" output.check - format.bvolume output - format.number.series output - address empty$ - { editor empty$ - 'skip$ - { organization output } - if$ - publisher output - format.date "year" output.check - } - { address output.nonnull - format.date "year" output.check - editor empty$ - 'skip$ - { organization output } - if$ - publisher output - } - if$ - new.block - note output - fin.entry -} - -FUNCTION {techreport} -{ output.bibitem - format.authors "author" output.check - format.title "title" output.check - format.tr.number output.nonnull - institution "institution" output.check - address output - format.date "year" output.check - new.block - note output - fin.entry -} - -FUNCTION {unpublished} -{ output.bibitem - format.authors "author" output.check - format.title "title" output.check - new.block - note "note" output.check - format.date output - fin.entry -} - -FUNCTION {default.type} { misc } - -MACRO {jan} {"Jan."} - -MACRO {feb} {"Feb."} - -MACRO {mar} {"Mar."} - -MACRO {apr} {"Apr."} - -MACRO {may} {"May"} - -MACRO {jun} {"June"} - -MACRO {jul} {"July"} - -MACRO {aug} {"Aug."} - -MACRO {sep} {"Sept."} - -MACRO {oct} {"Oct."} - -MACRO {nov} {"Nov."} - -MACRO {dec} {"Dec."} - -MACRO {acmcs} {"ACM Comput. Surveys"} - -MACRO {acta} {"Acta Inf."} - -MACRO {cacm} {"Comm. ACM"} - -MACRO {ibmjrd} {"IBM J. Res. Dev."} - -MACRO {ibmsj} {"IBM Syst.~J."} - -MACRO {ieeese} {"IEEE Trans. Softw. Eng."} - -MACRO {ieeetc} {"IEEE Trans. Comput."} - -MACRO {ieeetcad} - {"IEEE Trans. Comput.-Aided Design Integrated Circuits"} - -MACRO {ipl} {"Inf. Process. Lett."} - -MACRO {jacm} {"J.~Assoc. Comput. Mach."} - -MACRO {jcss} {"J.~Comput. System Sci."} - -MACRO {scp} {"Sci. Comput. Programming"} - -MACRO {sicomp} {"SIAM J. Comput."} - -MACRO {tocs} {"ACM Trans. Comput. Syst."} - -MACRO {tods} {"ACM Trans. Database Syst."} - -MACRO {tog} {"ACM Trans. Gr."} - -MACRO {toms} {"ACM Trans. Math. Softw."} - -MACRO {toois} {"ACM Trans. Office Inf. Syst."} - -MACRO {toplas} {"ACM Trans. Prog. Lang. Syst."} - -MACRO {tcs} {"Theoretical Comput. Sci."} - -READ - -FUNCTION {sortify} -{ purify$ - "l" change.case$ -} - -INTEGERS { len } - -FUNCTION {chop.word} -{ 's := - 'len := - s #1 len substring$ = - { s len #1 + global.max$ substring$ } - 's - if$ -} - -FUNCTION {sort.format.names} -{ 's := - #1 'nameptr := - "" - s num.names$ 'numnames := - numnames 'namesleft := - { namesleft #0 > } - { nameptr #1 > - { " " * } - 'skip$ - if$ - s nameptr "{vv{ } }{ll{ }}{ f{ }}{ jj{ }}" format.name$ 't := - nameptr numnames = t "others" = and - { "et al" * } - { t sortify * } - if$ - nameptr #1 + 'nameptr := - namesleft #1 - 'namesleft := - } - while$ -} - -FUNCTION {sort.format.title} -{ 't := - "A " #2 - "An " #3 - "The " #4 t chop.word - chop.word - chop.word - sortify - #1 global.max$ substring$ -} - -FUNCTION {author.sort} -{ author empty$ - { key empty$ - { "to sort, need author or key in " cite$ * warning$ - "" - } - { key sortify } - if$ - } - { author sort.format.names } - if$ -} - -FUNCTION {author.editor.sort} -{ author empty$ - { editor empty$ - { key empty$ - { "to sort, need author, editor, or key in " cite$ * warning$ - "" - } - { key sortify } - if$ - } - { editor sort.format.names } - if$ - } - { author sort.format.names } - if$ -} - -FUNCTION {author.organization.sort} -{ author empty$ - { organization empty$ - { key empty$ - { "to sort, need author, organization, or key in " cite$ * warning$ - "" - } - { key sortify } - if$ - } - { "The " #4 organization chop.word sortify } - if$ - } - { author sort.format.names } - if$ -} - -FUNCTION {editor.organization.sort} -{ editor empty$ - { organization empty$ - { key empty$ - { "to sort, need editor, organization, or key in " cite$ * warning$ - "" - } - { key sortify } - if$ - } - { "The " #4 organization chop.word sortify } - if$ - } - { editor sort.format.names } - if$ -} - -FUNCTION {presort} -{ type$ "book" = - type$ "inbook" = - or - 'author.editor.sort - { type$ "proceedings" = - 'editor.organization.sort - { type$ "manual" = - 'author.organization.sort - 'author.sort - if$ - } - if$ - } - if$ - " " - * - year field.or.null sortify - * - " " - * - title field.or.null - sort.format.title - * - #1 entry.max$ substring$ - 'sort.key$ := -} - -ITERATE {presort} - -SORT - -STRINGS { longest.label } - -INTEGERS { number.label longest.label.width } - -FUNCTION {initialize.longest.label} -{ "" 'longest.label := - #1 'number.label := - #0 'longest.label.width := -} - -FUNCTION {longest.label.pass} -{ number.label int.to.str$ 'label := - number.label #1 + 'number.label := - label width$ longest.label.width > - { label 'longest.label := - label width$ 'longest.label.width := - } - 'skip$ - if$ -} - -EXECUTE {initialize.longest.label} - -ITERATE {longest.label.pass} - -FUNCTION {begin.bib} -{ preamble$ empty$ - 'skip$ - { preamble$ write$ newline$ } - if$ - "\begin{thebibliography}{" longest.label * "}" * write$ newline$ -} - -EXECUTE {begin.bib} - -EXECUTE {init.state.consts} - -EXECUTE {init.last.authors} - -ITERATE {call.type$} - -FUNCTION {end.bib} -{ newline$ - "\end{thebibliography}" write$ newline$ -} - -EXECUTE {end.bib}
\ No newline at end of file diff --git a/Master/texmf-dist/source/latex/siam/ltexpprt.all b/Master/texmf-dist/source/latex/siam/ltexpprt.all deleted file mode 100644 index 907e77cfeec..00000000000 --- a/Master/texmf-dist/source/latex/siam/ltexpprt.all +++ /dev/null @@ -1,702 +0,0 @@ -%% This is ltexpprt.all. This file is to be used for creating a paper -%% in the ACM/SIAM Preprint series with LaTeX. It consists of the following -%% two files: -%% -%% ltexpprt.tex ---- an example and documentation file -%% ltexpprt.sty ---- the macro file -%% -%% To use, cut this file apart at the appropriate places. You can run the -%% example file with the macros to get sample output. -%% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%% CUT HERE %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% -% -%%%%%%%%%%%%%%%%%%%%%%%%%% ltexpprt.tex %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% -% This is ltexpprt.tex, an example file for use with the SIAM LaTeX -% Preprint Series macros. It is designed to provide double-column output. -% Please take the time to read the following comments, as they document -% how to use these macros. This file can be composed and printed out for -% use as sample output. - -% Any comments or questions regarding these macros should be directed to: -% -% Corey Gray -% SIAM -% 3600 University City Science Center -% Philadelphia, PA 19104-2688 -% USA -% Telephone: (215) 382-9800 -% Fax: (215) 386-7999 -% e-mail: gray@siam.org - - -% This file is to be used as an example for style only. It should not be read -% for content. - -%%%%%%%%%%%%%%% PLEASE NOTE THE FOLLOWING STYLE RESTRICTIONS %%%%%%%%%%%%%%% - -%% 1. There are no new tags. Existing LaTeX tags have been formatted to match -%% the Preprint series style. -%% -%% 2. You must use \cite in the text to mark your reference citations and -%% \bibitem in the listing of references at the end of your chapter. See -%% the examples in the following file. If you are using BibTeX, please -%% supply the bst file with the manuscript file. -%% -%% 3. Unless otherwise stated by your editor, do your chapter as if it -%% is Chapter 1. -%% If you know which number your chapter is, you must do the following: -%% -%% Use the \setcounter command to set the counters for chapter, -%% section, and page number to the appropriate number. The counter -%% for chapter is incremental, so it should be set one less than -%% the actual chapter number. The section counter is not -%% incremental. Set the page counter to 1. The following example -%% is set up as if it were chapter 3. Please note the placement of -%% the three \setcounter commands and follow it exactly. -%% -%% 4. This macro is set up for two levels of headings (\section and -%% \subsection). The macro will automatically number the headings for you. -%% -%% 5. The running heads are defined by the \markboth command. The left running -%% head (the first field of the \markboth command) should be defined with -%% the authors names. The right running head (the second field of the -%% \markboth command) should be defined with the title (or shortened title) -%% of your chapter. Neither running head may be more than 40 characters. -%% -%% 6. Theorems, Lemmas, Definitions, etc. are to be triple numbered, -%% indicating the chapter, section, and the occurence of that element -%% within that section. (For example, the first theorem in the second -%% section of chapter three would be numbered 3.2.1. The macro will -%% automatically do the numbering for you. -%% -%% 7. Figures, equations, and tables must be double-numbered indicating -%% chapter and occurence. Use existing LaTeX tags for these elements. -%% Numbering will be done automatically. -%% -%% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - - - -\documentstyle[twoside,leqno,twocolumn,ltexpprt]{article} - -\begin{document} - - -%\setcounter{chapter}{2} % If you are doing your chapter as chapter one, -%\setcounter{section}{3} % comment these two lines out. - -\title{\large\bf Chapter 1 \\ -\Large SIAM/ACM Preprint Series Macros for -Use With LaTeX\thanks{Supported by GSF grants ABC123, DEF456, and GHI789.}} -\author{Corey Gray\thanks{Society for Industrial and Applied Mathematics.} \\ -\and -Tricia Manning\thanks{Society for Industrial and Applied Mathematics.}} -\date{} - -\maketitle - -\pagestyle{myheadings} -\markboth{AUTHORS NAMES}{CHAPTER TITLE} - -%\pagenumbering{arabic} -%\setcounter{page}{1}%Leave this line commented out. - -\begin{abstract} \small\baselineskip=9pt This is the text of my abstract. It is a brief -description of my -paper, outlining the purposes and goals I am trying to address.\end{abstract} - -\section{Problem Specification.}In this paper, we consider the solution of the $N \times -N$ linear -system -\begin{equation} \label{e1.1} -A x = b -\end{equation} -where $A$ is large, sparse, symmetric, and positive definite. We consider -the direct solution of (\ref{e1.1}) by means of general sparse Gaussian -elimination. In such a procedure, we find a permutation matrix $P$, and -compute the decomposition -\[ -P A P^{t} = L D L^{t} -\] -where $L$ is unit lower triangular and $D$ is diagonal. - - -\section{Design Considerations.}Several good ordering algorithms (nested dissection and -minimum degree) -are available for computing $P$ \cite{GEORGELIU}, \cite{ROSE72}. -Since our interest here does not -focus directly on the ordering, we assume for convenience that $P=I$, -or that $A$ has been preordered to reflect an appropriate choice of $P$. - -Our purpose here is to examine the nonnumerical complexity of the -sparse elimination algorithm given in \cite{BANKSMITH}. -As was shown there, a general sparse elimination scheme based on the -bordering algorithm requires less storage for pointers and -row/column indices than more traditional implementations of general -sparse elimination. This is accomplished by exploiting the m-tree, -a particular spanning tree for the graph of the filled-in matrix. - -\begin{theorem} The method was extended to three -dimensions. For the standard multigrid -coarsening -(in which, for a given grid, the next coarser grid has $1/8$ -as many points), anisotropic problems require plane -relaxation to -obtain a good smoothing factor.\end{theorem} - -Our purpose here is to examine the nonnumerical complexity of the -sparse elimination algorithm given in \cite{BANKSMITH}. -As was shown there, a general sparse elimination scheme based on the -bordering algorithm requires less storage for pointers and -row/column indices than more traditional implementations of general -sparse elimination. This is accomplished by exploiting the m-tree, -a particular spanning tree for the graph of the filled-in matrix. -Several good ordering algorithms (nested dissection and minimum degree) -are available for computing $P$ \cite{GEORGELIU}, \cite{ROSE72}. -Since our interest here does not -focus directly on the ordering, we assume for convenience that $P=I$, -or that $A$ has been preordered to reflect an appropriate choice of $P$. - -\begin{proof} In this paper we consider two methods. The first method -is -basically the method considered with two differences: -first, we perform plane relaxation by a two-dimensional -multigrid method, and second, we use a slightly different -choice of -interpolation operator, which improves performance -for nearly singular problems. In the second method coarsening -is done by successively coarsening in each of the three -independent variables and then ignoring the intermediate -grids; this artifice simplifies coding considerably. -\end{proof} - -Our purpose here is to examine the nonnumerical complexity of the -sparse elimination algorithm given in \cite{BANKSMITH}. -As was shown there, a general sparse elimination scheme based on the -bordering algorithm requires less storage for pointers and -row/column indices than more traditional implementations of general -sparse elimination. This is accomplished by exploiting the m-tree, -a particular spanning tree for the graph of the filled-in matrix. - -\begin{Definition}{\rm We describe the two methods in \S 1.2. In \S\ 1.3. we -discuss -some remaining details.} -\end{Definition} - -Our purpose here is to examine the nonnumerical complexity of the -sparse elimination algorithm given in \cite{BANKSMITH}. -As was shown there, a general sparse elimination scheme based on the -bordering algorithm requires less storage for pointers and -row/column indices than more traditional implementations of general -sparse elimination. This is accomplished by exploiting the m-tree, -a particular spanning tree for the graph of the filled-in matrix. -Several good ordering algorithms (nested dissection and minimum degree) -are available for computing $P$ \cite{GEORGELIU}, \cite{ROSE72}. -Since our interest here does not -focus directly on the ordering, we assume for convenience that $P=I$, -or that $A$ has been preordered to reflect an appropriate choice of $P$. - -Our purpose here is to examine the nonnumerical complexity of the -sparse elimination algorithm given in \cite{BANKSMITH}. -As was shown there, a general sparse elimination scheme based on the -bordering algorithm requires less storage for pointers and -row/column indices than more traditional implementations of general -sparse elimination. - -\begin{lemma} We discuss first the choice for $I_{k-1}^k$ -which is a generalization. We assume that $G^{k-1}$ is -obtained -from $G^k$ -by standard coarsening; that is, if $G^k$ is a tensor product -grid $G_{x}^k \times G_{y}^k \times G_{z}^k$, -$G^{k-1}=G_{x}^{k-1} \times G_{y}^{k-1} \times G_{z}^{k-1}$, -where $G_{x}^{k-1}$ is obtained by deleting every other grid -point of $G_x^k$ and similarly for $G_{y}^k$ and $G_{z}^k$. -\end{lemma} - -To our knowledge, the m-tree previously has not been applied in this -fashion to the numerical factorization, but it has been used, -directly or indirectly, in several optimal order algorithms for -computing the fill-in during the symbolic factorization phase -[4] - [10], [5], [6]. In \S 1.3., we analyze the complexity of the old and new -approaches to the intersection problem for the special case of -an $n \times n$ grid ordered by nested dissection. The special -structure of this problem allows us to make exact estimates of -the complexity. To our knowledge, the m-tree previously has not been applied in this -fashion to the numerical factorization, but it has been used, -directly or indirectly, in several optimal order algorithms for -computing the fill-in during the symbolic factorization phase -[4] - [10], [5], [6]. - -In \S 1.2, we review the bordering algorithm, and introduce -the sorting and intersection problems that arise in the -sparse formulation of the algorithm. -In \S 1.3., we analyze the complexity of the old and new -approaches to the intersection problem for the special case of -an $n \times n$ grid ordered by nested dissection. The special -structure of this problem allows us to make exact estimates of -the complexity. To our knowledge, the m-tree previously has not been applied in this -fashion to the numerical factorization, but it has been used, -directly or indirectly, in several optimal order algorithms for -computing the fill-in during the symbolic factorization phase -[4] - [10], [5], [6]. - - -For the old approach, we show that the -complexity of the intersection problem is $O(n^{3})$, the same -as the complexity of the numerical computations. For the -new approach, the complexity of the second part is reduced to -$O(n^{2} (\log n)^{2})$. - -To our knowledge, the m-tree previously has not been applied in this -fashion to the numerical factorization, but it has been used, -directly or indirectly, in several optimal order algorithms for -computing the fill-in during the symbolic factorization phase -[4] - [10], [5], [6]. In \S 1.3., we analyze the complexity of the old and new -approaches to the intersection problem for the special case of -an $n \times n$ grid ordered by nested dissection. The special -structure of this problem allows us to make exact estimates of -the complexity. To our knowledge, the m-tree previously has not been applied in this -fashion to the numerical factorization, but it has been used, -directly or indirectly, in several optimal order algorithms for -computing the fill-in during the symbolic factorization phase -[4] - [10], [5], [6]. -This is accomplished by exploiting the m-tree, -a particular spanning tree for the graph of the filled-in matrix. -To our knowledge, the m-tree previously has not been applied in this -fashion to the numerical factorization, but it has been used, -directly or indirectly, in several optimal order algorithms for -computing the fill-in during the symbolic factorization phase -\cite{EISENSTAT} - \cite{LIU2}, \cite{ROSE76}, \cite{SCHREIBER}. - -\subsection{Robustness.}\ We do not -attempt to present an overview -here, but rather attempt to focus on those results that -are relevant to our particular algorithm. -This section assumes prior knowledge of the role of graph theory -in sparse Gaussian elimination; surveys of this role are -available in \cite{ROSE72} and \cite{GEORGELIU}. More general -discussions of elimination trees are given in -\cite{LAW} - \cite{LIU2}, \cite{SCHREIBER}. -Thus, at the $k$th stage, the bordering algorithm consists of -solving the lower triangular system -\begin{equation} \label{1.2} - L_{k-1}v = c -\end{equation} -and setting -\begin{eqnarray} -\ell &=& D^{-1}_{k-1}v , \\ -\delta &=& \alpha - \ell^{t} v . -\end{eqnarray} - -\begin{figure} -\vspace{14pc} -\caption{This is a figure 1.1.} -\end{figure} - -\section{Robustness.} We do not -attempt to present an overview -here, but rather attempt to focus on those results that -are relevant to our particular algorithm. - -\subsection{Versatility.}\ The special -structure of this problem allows us to make exact estimates of -the complexity. For the old approach, we show that the -complexity of the intersection problem is $O(n^{3})$, the same -as the complexity of the numerical computations -\cite{GEORGELIU}, \cite{ROSEWHITTEN}. For the -new approach, the complexity of the second part is reduced to -$O(n^{2} (\log n)^{2})$. - -To our knowledge, the m-tree previously has not been applied in this -fashion to the numerical factorization, but it has been used, -directly or indirectly, in several optimal order algorithms for -computing the fill-in during the symbolic factorization phase -[4] - [10], [5], [6]. In \S 1.3., we analyze the complexity of the old and new -approaches to the intersection problem for the special case of -an $n \times n$ grid ordered by nested dissection. The special -structure of this problem allows us to make exact estimates of -the complexity. To our knowledge, the m-tree previously has not been applied in this -fashion to the numerical factorization, but it has been used, -directly or indirectly, in several optimal order algorithms for -computing the fill-in during the symbolic factorization phase -[4] - [10], [5], [6]. - -In \S 1.2, we review the bordering algorithm, and introduce -the sorting and intersection problems that arise in the -sparse formulation of the algorithm. -In \S 1.3., we analyze the complexity of the old and new -approaches to the intersection problem for the special case of -an $n \times n$ grid ordered by nested dissection. The special -structure of this problem allows us to make exact estimates of -the complexity. To our knowledge, the m-tree previously has not been applied in this -fashion to the numerical factorization, but it has been used, -directly or indirectly, in several optimal order algorithms for -computing the fill-in during the symbolic factorization phase -[4] - [10], [5], [6]. - - -For the old approach, we show that the -complexity of the intersection problem is $O(n^{3})$, the same -as the complexity of the numerical computations. For the -new approach, the complexity of the second part is reduced to -$O(n^{2} (\log n)^{2})$. - -To our knowledge, the m-tree previously has not been applied in this -fashion to the numerical factorization, but it has been used, -directly or indirectly, in several optimal order algorithms for -computing the fill-in during the symbolic factorization phase -[4] - [10], [5], [6]. In \S 1.3., we analyze the complexity of the old and new -approaches to the intersection problem for the special case of -an $n \times n$ grid ordered by nested dissection. The special -structure of this problem allows us to make exact estimates of -the complexity. To our knowledge, the m-tree previously has not been applied in this -fashion to the numerical factorization, but it has been used, -directly or indirectly, in several optimal order algorithms for -computing the fill-in during the symbolic factorization phase -[4] - [10], [5], [6]. -This is accomplished by exploiting the m-tree, -a particular spanning tree for the graph of the filled-in matrix. -To our knowledge, the m-tree previously has not been applied in this -fashion to the numerical factorization, but it has been used, -directly or indirectly, in several optimal order algorithms for -computing the fill-in during the symbolic factorization phase -\cite{EISENSTAT} - \cite{LIU2}, \cite{ROSE76}, \cite{SCHREIBER}. - -\begin{thebibliography}{99} - -%\bibitem{GUIDE} -%R.~E. Bank, {\em PLTMG users' guide, edition 5.0}, tech. report, -% Department of Mathematics, University of California, San Diego, CA, 1988. - -%\bibitem{HBMG} -%R.~E. Bank, T.~F. Dupont, and H.~Yserentant, {\em The hierarchical basis -% multigrid method}, Numer. Math., 52 (1988), pp.~427--458. - -\bibitem{BANKSMITH} -R.~E. Bank and R.~K. Smith, {\em General sparse elimination requires no - permanent integer storage}, SIAM J. Sci. Stat. Comput., 8 (1987), - pp.~574--584. - -\bibitem{EISENSTAT} -S.~C. Eisenstat, M.~C. Gursky, M.~Schultz, and A.~Sherman, {\em - Algorithms and data structures for sparse symmetric gaussian elimination}, - SIAM J. Sci. Stat. Comput., 2 (1982), pp.~225--237. - -\bibitem{GEORGELIU} -A.~George and J.~Liu, {\em Computer Solution of Large Sparse Positive - Definite Systems}, Prentice Hall, Englewood Cliffs, NJ, 1981. - -\bibitem{LAW} -K.~H. Law and S.~J. Fenves, {\em A node addition model for symbolic - factorization}, ACM TOMS, 12 (1986), pp.~37--50. - -\bibitem{LIU} -J.~W.~H. Liu, {\em A compact row storage scheme for cholesky factors - using elimination trees}, ACM TOMS, 12 (1986), pp.~127--148. - -\bibitem{LIU2} -\sameauthor , {\em The role of - elimination trees in sparse factorization}, Tech. Report CS-87-12,Department - of Computer Science, York University, Ontario, Canada, 1987. - -\bibitem{ROSE72} -D.~J. Rose, {\em A graph theoretic study of the numeric solution of - sparse positive definite systems}, in Graph Theory and Computing, AcademicΠPress, New -York, 1972. - -\bibitem{ROSE76} -D.~J. Rose, R.~E. Tarjan, and G.~S. Lueker, {\em Algorithmic aspects of - vertex elimination on graphs}, SIAM J. Comput., 5 (1976), pp.~226--283. - -\bibitem{ROSEWHITTEN} -D.~J. Rose and G.~F. Whitten, {\em A recursive analysis of disection - strategies}, in Sparse Matrix Computations, Academic Press, New York, 1976. - -\bibitem{SCHREIBER} -R.~Schrieber, {\em A new implementation of sparse gaussian elimination}, - ACM TOMS, 8 (1982), pp.~256--276. - -\end{thebibliography} -\end{document} - -% End of ltexpprt.tex -% -% -% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% CUT HERE %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% -% -% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% ltexpprt.sty %%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% -% This is ltexpprt.sty, a file of macros and definitions for creating a -% chapter for publication in the ACM/SIAM Preprint series using LaTeX. -% It is designed to produce double-column output. -% This file may be freely distributed but may not be altered in any way. -% Any comments or questions regarding these macros should be directed to: - -% Corey Gray -% SIAM -% 3600 University City Science Center -% Philadelphia, PA 19104-2688 -% USA -% Telephone: (215) 382-9800 -% Fax: (215) 386-7999 -% e-mail: gray@siam.org - - -% Report the version. -\message{*** ACM/SIAM LaTeX Preprint Series macro package, version 1.0, -September 24,1990 ***} - - -\pretolerance=800 -\tolerance=10000 -\sloppy - -\voffset=-.5in -\hoffset=-.5in -\vsize=55pc -\hsize=41pc -\baselineskip=14pt -\footskip=18pt -\topmargin 24pt -\headheight 12pt -\headsep 17pt -\textheight 52.5pc \advance\textheight by \topskip -\textwidth 41pc -\parskip 0pt -\parindent 18pt - -\font\tensmc=cmcsc10 -\def\smc{\tensmc} - -%% footnotes to be set 8/10 -\def\footnotesize{\@setsize\footnotesize{10pt}\viiipt\@viiipt - % \indent - \abovedisplayskip \z@ - \belowdisplayskip\z@ - \abovedisplayshortskip\abovedisplayskip - \belowdisplayshortskip\belowdisplayshortskip - \def\@listi{\leftmargin\leftmargini \topsep 3pt plus 1pt minus 1pt - \parsep 2pt plus 1pt minus 1pt - \itemsep \parsep}} - -\let\referencesize\footnotesize - -\footnotesep 0pt - -\skip\footins 12pt plus 12pt - -\def\footnoterule{\kern3\p@ \hrule width 3em} % the \hrule is .4pt high - -\def\ps@plain{\let\@mkboth\@gobbletwo - \def\@oddfoot{{\hfil\small\thepage\hfil}}% - \def\@oddhead{} - \def\@evenhead{}\def\@evenfoot{}} - - - - - -\def\ps@headings{\let\@mkboth\markboth - \def\@oddfoot{}\def\@evenfoot{}% - \def\@evenhead{{\rm\thepage}\hfil{\small\leftmark}}% - \def\@oddhead{{\noindent\small\rightmark}\hfil{\rm\thepage}}% - - - -\def\ps@myheadings{\let\@mkboth\@gobbletwo - \def\@oddfoot{}\def\@evenfoot{}% - \def\@oddhead{\rlap{\normalsize\rm\rightmark}\hfil{small\thepage}}% - \def\@evenhead%{\hfil{\small\@chapapp}\ - {\small\thepage}\hfil\llap{\normalsize\rm\leftmark}}% - \def\chaptermark##1{}% - \def\sectionmark##1{}\def\subsectionmark##1{}} - - -\def\theequation{\arabic{section}.\arabic{equation}} - - -\def\section{\@startsection{section}{1}{0pt}{-12pt}{3pt}{\hyphenpenalty=\@M -\exhyphenpenalty=\@M\normalsize\bf}} -\def\subsection{\@startsection{subsection}{2}{0pt}{-12pt}{0pt}{\normalsize\bf} -} -\def\subsubsection{\@startsection - {subsubsection}{3}{0pt}{-12pt}{0pt}{\normalsize\bf}} -\def\paragraph{\@startsection - {paragraph}{4}{\parindent}{0pt}{0pt}{\normalsize\bf}} -\def\subparagraph{\@startsection - {subparagraph}{4}{\parindent}{0pt}{0pt}{\normalsize\bf}} - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% % -% THEOREMS, PROOFS, ALGORITHMS % -% % -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -%%% defined proof environment by theorem model (took out counter) - -\def\newproof#1{\@nprf{#1}} - -\def\@nprf#1#2{\@xnprf{#1}{#2}} - -\def\@xnprf#1#2{\expandafter\@ifdefinable\csname #1\endcsname -\global\@namedef{#1}{\@prf{#1}{#2}}\global\@namedef{end#1}{\@endproof}} - -\def\@prf#1#2{\@xprf{#1}{#2}} - -\def\@xprf#1#2{\@beginproof{#2}{\csname the#1\endcsname}\ignorespaces} - - - -%%% defined algorithm environment by theorem model - -\def\newalgorithm#1{\@ifnextchar[{\@oalg{#1}}{\@nalg{#1}}} - -\def\@nalg#1#2{% -\@ifnextchar[{\@xnalg{#1}{#2}}{\@ynalg{#1}{#2}}} - -\def\@xnalg#1#2[#3]{\expandafter\@ifdefinable\csname #1\endcsname -{\@definecounter{#1}\@addtoreset{#1}{#3}% -\expandafter\xdef\csname the#1\endcsname{\expandafter\noexpand - \csname the#3\endcsname \@thmcountersep \@thmcounter{#1}}% -\global\@namedef{#1}{\@alg{#1}{#2}}\global\@namedef{end#1}{\@endalgorithm}}} - -\def\@ynalg#1#2{\expandafter\@ifdefinable\csname #1\endcsname -{\@definecounter{#1}% -\expandafter\xdef\csname the#1\endcsname{\@thmcounter{#1}}% -\global\@namedef{#1}{\@alg{#1}{#2}}\global\@namedef{end#1}{\@endalgorithm}}} - -\def\@oalg#1[#2]#3{\expandafter\@ifdefinable\csname #1\endcsname - {\global\@namedef{the#1}{\@nameuse{the#2}}% -\global\@namedef{#1}{\@alg{#2}{#3}}% -\global\@namedef{end#1}{\@endalgorithm}}} - -\def\@alg#1#2{\refstepcounter - {#1}\@ifnextchar[{\@yalg{#1}{#2}}{\@xalg{#1}{#2}}} - -\def\@xalg#1#2{\@beginalgorithm{#2}{\csname the#1\endcsname}\ignorespaces} -\def\@yalg#1#2[#3]{\@opargbeginalgorithm{#2}{\csname - the#1\endcsname}{#3}\ignorespaces} - - - - -\def\@beginproof#1{\rm \trivlist \item[\hskip \labelsep{\it #1.\/}]} -\def\@endproof{\outerparskip 0pt\endtrivlist} - -\def\@begintheorem#1#2{\it \trivlist \item[\hskip \labelsep{\sc #1\ #2.}]} -\def\@opargbegintheorem#1#2#3{\it \trivlist - \item[\hskip \labelsep{\sc #1\ #2.\ (#3)}]} -\def\@endtheorem{\outerparskip 0pt\endtrivlist} - -%\def\@begindefinition#1#2{\rm \trivlist \item[\hskip \labelsep{\sc #1\ #2.}]} -%\def\@opargbegindefinition#1#2#3{\rm \trivlist -% \item[\hskip \labelsep{\sc #1\ #2.\ (#3)}]} -%\def\@enddefinition{\outerparskip 0pt\endtrivlist} - - -\def\@beginalgorithm#1#2{\rm \trivlist \item[\hskip \labelsep{\sc #1\ #2.}]} -\def\@opargbeginalgorithm#1#2#3{\rm \trivlist - \item[\hskip \labelsep{\sc #1\ #2.\ (#3)}]} -\def\@endalgorithm{\outerparskip 6pt\endtrivlist} - - -\newskip\outerparskip - -\def\trivlist{\parsep\outerparskip - \@trivlist \labelwidth\z@ \leftmargin\z@ - \itemindent\parindent \def\makelabel##1{##1}} - -\def\@trivlist{\topsep=0pt\@topsepadd\topsep - \if@noskipsec \leavevmode \fi - \ifvmode \advance\@topsepadd\partopsep \else \unskip\par\fi - \if@inlabel \@noparitemtrue \@noparlisttrue - \else \@noparlistfalse \@topsep\@topsepadd \fi - \advance\@topsep \parskip - \leftskip\z@\rightskip\@rightskip \parfillskip\@flushglue - \@setpar{\if@newlist\else{\@@par}\fi}% - \global\@newlisttrue \@outerparskip\parskip} - - -\def\endtrivlist{\if@newlist\@noitemerr\fi - \if@inlabel\indent\fi - \ifhmode\unskip \par\fi - \if@noparlist \else - \ifdim\lastskip >\z@ \@tempskipa\lastskip \vskip -\lastskip - \advance\@tempskipa\parskip \advance\@tempskipa -\@outerparskip - \vskip\@tempskipa - \fi\@endparenv\fi - \vskip\outerparskip} - - - - \newproof{@proof}{Proof} - \newenvironment{proof}{\begin{@proof}}{\end{@proof}} - - \newtheorem{@theorem}{Theorem}[section] - \newenvironment{theorem}{\begin{@theorem}}{\end{@theorem}} - - \newalgorithm{@algorithm}{Algorithm}[section] - \newenvironment{algorithm}{\begin{@algorithm}}{\end{@algorithm}} - - - -\newtheorem{lemma}{Lemma}[section] -\newtheorem{fact}{Fact}[section] -\newtheorem{corollary}{Corollary}[section] -\newtheorem{axiom}{Axiom}[section] -\newtheorem{cond}{Condition}[section] -\newtheorem{property}{Property}[section] -\newtheorem{proposition}{Proposition}[section] - -\newtheorem{Conjecture}{Conjecture}[section] -%\newtheorem{Corollary}[Theorem]{Corollary} -\newtheorem{Definition}{Definition}[section] -\newtheorem{Lemma}{Lemma}[section] -\newtheorem{Remark}{Remark}[section] - -\newproof{Example}{Example} -\newproof{Method}{Method} -\newproof{Exercise}{Exercise} - - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% %% -%% BIBLIOGRAPHY %% -%% %% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - - -\def\thebibliography#1{% -%\cleardoublepage -\parindent 0em -\vspace{6pt} -\begin{flushleft}\normalsize\bf References\end{flushleft} -\addvspace{3pt}\nopagebreak\list - %% default is no labels, for those not using \cite or BibTeX -% {[\arabic{enumi}]} {\settowidth\labelwidth{[#1]} -{[\arabic{enumi}]}{\settowidth\labelwidth{mm} -\leftmargin\labelwidth - \advance\leftmargin\labelsep - \usecounter{enumi}\@bibsetup} -\def\newblock{\hskip .11em plus .33em minus -.07em} - \sloppy\clubpenalty4000\widowpenalty4000 - \sfcode`\.=1000\relax} - -%% setup 8/10 type -\def\@bibsetup{\itemindent=0pt \itemsep=0pt \parsep=0pt -\small} - -\def\sameauthor{\leavevmode\vrule height 2pt depth -1.6pt width 23pt} - -% -%% End of ltexpprt.sty -% -%%%%%%%%%%%%%%%%%%%%%%%%% End of ltexpprt.all %%%%%%%%%%%%%%%%%%%%%%% -
\ No newline at end of file diff --git a/Master/texmf-dist/source/latex/siam/ltexproc.all b/Master/texmf-dist/source/latex/siam/ltexproc.all deleted file mode 100644 index 61283eec0aa..00000000000 --- a/Master/texmf-dist/source/latex/siam/ltexproc.all +++ /dev/null @@ -1,1784 +0,0 @@ - - -This file constitutes the full distribution for SIAM Proceedings -Series LaTeX version macros. The files included here are: - -ltexproc.tex (An example file, also containing documentation) - -ltexproc.sty (The style file) - -siamproc.bst (for BiBTeX users) - -To use these macros, separate the files at the indicated cut lines. - -%%%%%%%%%%%%%%%%%%%%%%%%CUT HERE%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -% This is ltexproc.tex, an example file for use with the SIAM LaTeX -% Proceedings Series macros. -% Please take the time to read the following comments, as they describe -% how to use these macros. This file can be composed and printed out for -% use as sample output. - -% Any comments or questions regarding these macros should be directed to: -% -% Corey Gray -% SIAM -% 3600 University City Science Center -% Philadelphia, PA 19104-2688 -% USA -% Telephone: (215) 382-9800 -% Fax: (215) 386-7999 -% e-mail: gray@siam.org - - -% This file is to be used as an example for style only. It should not be read -% for content. - -%%%%%%%%%%%%%%% PLEASE NOTE THE FOLLOWING STYLE RESTRICTIONS %%%%%%%%%%%%%%% - -%% 1. There are no new tags. Existing LaTeX tags have been formatted to -%% match the Proceedings series style. -%% -%% 2. You must use \cite in the text to mark your reference citations and -%% \bibitem in the listing of references at the end of your chapter. See -%% the examples in the following file. The file siamproc.bst has been -%% included for use with BiBTeX. Please be sure to include the appropriate -%% .bib file with BiBTeX submissions. You may also submit the .bbl file -%% instead of the .bib file. -%% -%% 3. Unless otherwise stated by your editor, do your chapter as if it -%% is Chapter 1. The appropriate chapter number will be included during -%% the production of the proceedings. -%% -%% 4. This macro is set up for three levels of headings (\section, -%% \subsection, and \subsubsection). The macro will automatically number -%% the headings for you. -%% -%% 5. The running heads are indicated by the \markboth command. Please -%% define the running heads by placing the authors last names in the -%% first field and the title of the paper in the second field. -%% They should be typed initial cap and lower case. Please see the example. -%% Neither field can contain more than 50 characters including spaces, -%% so please use a shortened version of the title if necessary. For -%% papers with multiple authors please follow these rules; for -%% two authors type {Author 1 and Author 2}; for more that two authors type -%% {Author 1 et al.}. -%% -%% 6. Theorems, Lemmas, Definitions, etc. are to be double-numbered, -%% indicating the section and the occurrence of that element -%% within that section. (For example, the first theorem in the second -%% section would be numbered 2.1. The macro will -%% automatically do the numbering for you. -%% -%% 7. Proofs are handled with the commands \begin{proof}\end{proof}. -%% If you wish to use an end of proof box, use \qed preceding \end{proof}. -%% The example uses one. It is not required. -%% -%% 8. Figures, equations, and tables must be single-numbered. All equation -%% numbers are to be on the left. Figure captions should be placed under -%% the figures they pertain to. Table captions should be placed above -%% the tables. Use existing LaTeX tags for these elements. Numbering of -%% these elements will be done automatically. SIAM supports the use of -%% psfig for including Postscript figures. All Postscript figures should be -%% sent as separate files. A hardcopy version of all Postscript figures -%% is also required. See note regarding this under How to Submit Your Paper. -%% -%% 9. Grant information and author affiliations. -%% This information is included in the file with the two commands, -%% \thanks and \footnotemark []. (See example). The \thanks command -%% produces a footnote for the title or author, and places the -%% appropriate footnote symbol with the title or author and at the -%% bottom of the page. The \footnotemark [] command allows the use of -%% duplicate footnote symbols. This macro follows the normal LaTeX order -%% of footnote symbols. Below is a list of these symbols, and their -%% corresponding footnotemark: -%% -%% asterisk \footnotemark[1] -%% single-dagger \footnotemark[2] -%% double-dagger \footnotemark[3] -%% section sign \footnotemark[4] -%% paragraph \footnotemark[5] -%% parallel \footnotemark[6] -%% double asterisk \footnotemark[7] -%% double single-dagger \footnotemark[8] -%% double double-dagger \footnotemark[9] -%% -%% The following general rules for grants and affiliations apply: -%% a) If there is a single grant for the paper, then the grant -%% information should be footnoted to the title. -%% b) If there is more than one grant, include the grant information -%% with each author's affiliation. -%% c) If there are different grants for the paper but the authors share -%% the same affiliation, footnote the grant information to the title. -%% For example, The work of the first author was supported by xyz. -%% The work of the second author was supported by abc. And so on. -%% d) For authors sharing the same affiliation, use \thanks for the -%% first author with that affiliation and the appropriate -%% \footnotemark[] (from the list above) for all subsequent authors -%% with that affiliation. -%% -%% 10. Special fonts. -%% SIAM supports the use of AMS-TeX fonts version 2.0 and later. As -%% described in the manual for these fonts, they can be included by -%% \input{amssym.def} and \input{amssym.tex}. These macros are not yet -%% updated to make use of the New Font Selection Scheme (NFSS) of -%% Mittelbach and Schopf. To make these macros compatible with NFSS, use -%% the oldlfont style option. -%% -%% 11. How to Submit Your Paper. -%% The electronic version of your paper should be sent to proceed@siam.org. -%% A hardcopy version should also be submitted. Instructions are included -%% in your acceptance letter. Please be sure to send hardcopy -%% versions of any Postscript figures you have submitted electronically. -%% Be sure to return your signed Copyright Transfer Agreement. We cannot -%% publish your paper without it. -%% -%% -%% -%% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%- -%%% - - -\documentstyle[leqno,twoside,11pt,ltexproc]{article} %You must set up your - %\documentstyle line like this. - - -\begin{document} -\cleardoublepage -\pagestyle{myheadings} - -\title{Chapter 1\\ -SIAM Proceedings Series Macros\\ - for Use With LaTeX\thanks{Any information regarding grants should be placed -here.}} -\author{J. Corey Gray\thanks{Production Manager, Society for Industrial and Applied -Mathematics, Philadelphia, PA.} -\and -Tricia Manning\thanks{Publications Specialist, Society for Industrial and Applied -Mathematics, Philadelphia, PA.} -\and -Vickie Kearn\thanks{Publisher, Society for Industrial and Applied Mathematics, -Philadelphia, PA.}\\ -\and -Nancy Abbott\thanks{Design Supervisor, Society for Industrial and Applied -Mathematics, Philadelphia, PA} -\and -Sue Ciambrano\thanks{Acquisitions Editor, Society for Industrial and Applied -Mathematics, Philadelphia, PA} -\and -Paul Duggan\thanks{Composition Specialist, Society for Industrial and Applied -Mathematics, Philadelphia, PA} -\and -Robbi Anne Albert\thanks{Production Assistant, Society for Industrial and Applied -Mathematics, Philadelphia, PA} -\and -Jean Anderson\thanks{Composition Coordinator, Society for Industrial and Applied -Mathematics, Philadelphia, PA} -} -\date{} -\maketitle -\markboth{Gray et al.}{SIAM Proceedings Series Macros} % See section 5 above - % for explanation. -\pagenumbering{arabic} - -\begin{abstract}An equivalence is shown between realizability of input/output (i/o) operators by -rational control systems and high-order algebraic differential equations for -i/o pairs. This generalizes, to nonlinear systems, the equivalence -between autoregressive representations and finite dimensional linear -realizability. \end{abstract} -\section{Problem Specification}In this paper, we consider the solution of the $N \times -N$ linear -system -\begin{equation} \label{e1.1} -\cos \sin A x = b -\end{equation} -where $A$ is large, sparse, symmetric, and positive definite. We consider -the direct solution of (\ref{e1.1}) by means of general sparse Gaussian -elimination. In such a procedure, we find a permutation matrix $P$, and -compute the decomposition -\[ -P A P^{t} = L D L^{t} -\] -where $L$ is unit lower triangular and $D$ is diagonal. - - -\section{Design Considerations}Several good ordering algorithms (nested dissection and -minimum degree) -are available for computing $P$ \cite{GEORGELIU}, \cite{ROSE72}. -Since our interest here does not -focus directly on the ordering, we assume for convenience that $P=I$, -or that $A$ has been preordered to reflect an appropriate choice of $P$. - -Our purpose here is to examine the nonnumerical complexity of the -sparse elimination algorithm given in \cite{BANKSMITH}. -As was shown there, a general sparse elimination scheme based on the -bordering algorithm requires less storage for pointers and -row/column indices than more traditional implementations of general -sparse elimination. This is accomplished by exploiting the m-tree, -a particular spanning tree for the graph of the filled-in matrix. - -\begin{theorem} The method was extended to three -dimensions. For the standard multigrid -coarsening -(in which, for a given grid, the next coarser grid has $1/8$ -as many points), anisotropic problems require plane -relaxation to -obtain a good smoothing factor.\end{theorem} - -Several good ordering algorithms (nested dissection and minimum degree) -are available for computing $P$ \cite{GEORGELIU}, \cite{ROSE72}. -Since our interest here does not -focus directly on the ordering, we assume for convenience that $P=I$, -or that $A$ has been preordered to reflect an appropriate choice of $P$. - - -\begin{proof} In this paper we consider two methods. The first method -is -basically the method considered with two differences: -first, we perform plane relaxation by a two-dimensional -multigrid method, and second, we use a slightly different -choice of -interpolation operator, which improves performance -for nearly singular problems. In the second method coarsening -is done by successively coarsening in each of the three -independent variables and then ignoring the intermediate -grids; this artifice simplifies coding considerably.\qed -\end{proof} - -Our purpose here is to examine the nonnumerical complexity of the -sparse elimination algorithm given in \cite{BANKSMITH}. -As was shown there, a general sparse elimination scheme based on the -bordering algorithm requires less storage for pointers and -row/column indices than more traditional implementations of general -sparse elimination. This is accomplished by exploiting the m-tree, -a particular spanning tree for the graph of the filled-in matrix. - -\begin{Definition}{\rm We describe the two methods in \S 1.2. In \S\ 1.3. we -discuss -some remaining details.} -\end{Definition} - -\begin{figure} -\vspace*{24pc} -\caption{This is figure 1.} -\end{figure} - -Our purpose here is to examine the nonnumerical complexity of the -sparse elimination algorithm given in \cite{BANKSMITH}. -As was shown there, a general sparse elimination scheme based on the -bordering algorithm requires less storage for pointers and -row/column indices than more traditional implementations of general -sparse elimination. - -\begin{lemma} We discuss first the choice for $I_{k-1}^k$ -which is a generalization. We assume that $G^{k-1}$ is -obtained -from $G^k$ -by standard coarsening; that is, if $G^k$ is a tensor product -grid $G_{x}^k \times G_{y}^k \times G_{z}^k$, -$G^{k-1}=G_{x}^{k-1} \times G_{y}^{k-1} \times G_{z}^{k-1}$, -where $G_{x}^{k-1}$ is obtained by deleting every other grid -point of $G_x^k$ and similarly for $G_{y}^k$ and $G_{z}^k$. -\end{lemma} - -This is accomplished by exploiting the m-tree, -a particular spanning tree for the graph of the filled-in matrix. -To our knowledge, the m-tree previously has not been applied in this -fashion to the numerical factorization, but it has been used, -directly or indirectly, in several optimal order algorithms for -computing the fill-in during the symbolic factorization phase -\cite{EISENSTAT} - \cite{LIU2}, \cite{ROSE76}, \cite{SCHREIBER}. - -\subsection{Robustness} -We do not -attempt to present an overview -here, but rather attempt to focus on those results that -are relevant to our particular algorithm. -This section assumes prior knowledge of the role of graph theory -in sparse Gaussian elimination; surveys of this role are -available in \cite{ROSE72} and \cite{GEORGELIU}. More general -discussions of elimination trees are given in -\cite{LAW} - \cite{LIU2}, \cite{SCHREIBER}. -Thus, at the $k$th stage, the bordering algorithm consists of -solving the lower triangular system -\begin{equation} \label{1.2} - L_{k-1}v = c -\end{equation} -and setting -\begin{eqnarray} -\ell &=& D^{-1}_{k-1}v , \\ -\delta &=& \alpha - \ell^{t} v . -\end{eqnarray} - -\subsubsection{Versatility.} We do not -attempt to present an overview -here, but rather attempt to focus on those results that -are relevant to our particular algorithm. - -\section{Conclusions} The special -structure of this problem allows us to make exact estimates of -the complexity. For the old approach, we show that the -complexity of the intersection problem is $O(n^{3})$, the same -as the complexity of the numerical computations -\cite{GEORGELIU}, \cite{ROSEWHITTEN}. For the -new approach, the complexity of the second part is reduced to -$O(n^{2} (\log n)^{2})$. - -\begin{thebibliography}{99} - - -\bibitem{BANKSMITH} -R.~E. Bank and R.~K. Smith, {\em General sparse elimination requires no - permanent integer storage}, SIAM J. Sci. Stat. Comput., 8 (1987), - pp.~574--584. - -\bibitem{EISENSTAT} -S.~C. Eisenstat, M.~C. Gursky, M.~Schultz, and A.~Sherman, {\em - Algorithms and data structures for sparse symmetric gaussian elimination}, - SIAM J. Sci. Stat. Comput., 2 (1982), pp.~225--237. - -\bibitem{GEORGELIU} -A.~George and J.~Liu, {\em Computer Solution of Large Sparse Positive - Definite Systems}, Prentice Hall, Englewood Cliffs, NJ, 1981. - -\bibitem{LAW} -K.~H. Law and S.~J. Fenves, {\em A node addition model for symbolic - factorization}, ACM TOMS, 12 (1986), pp.~37--50. - -\bibitem{LIU} -J.~W.~H. Liu, {\em A compact row storage scheme for cholesky factors - using elimination trees}, ACM TOMS, 12 (1986), pp.~127--148. - -\bibitem{LIU2} -\sameauthor , {\em The role of - elimination trees in sparse factorization}, Tech. Report CS-87-12,Department - of Computer Science, York University, Ontario, Canada, 1987. - -\bibitem{ROSE72} -D.~J. Rose, {\em A graph theoretic study of the numeric solution of - sparse positive definite systems}, in Graph Theory and Computing, Academic Press, New -York, 1972. - -\bibitem{ROSE76} -D.~J. Rose, R.~E. Tarjan, and G.~S. Lueker, {\em Algorithmic aspects of - vertex elimination on graphs}, SIAM J. Comput., 5 (1976), pp.~226--283. - -\bibitem{ROSEWHITTEN} -D.~J. Rose and G.~F. Whitten, {\em A recursive analysis of disection - strategies}, in Sparse Matrix Computations, Academic Press, New York, 1976. - -\bibitem{SCHREIBER} -R.~Schreiber, {\em A new implementation of sparse gaussian elimination}, - ACM TOMS, 8 (1982), pp.~256--276. - -\end{thebibliography} - -\end{document} - -%%%%%%%%%%%%%%%%%%%%%%%%%%CUT HERE%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -% This is ltexproc.sty. -% This file may be freely distributed but may not be altered in any way. -% Any comments or questions regarding these macros should be directed to: - -% Corey Gray -% SIAM -% 3600 University City Science Center -% Philadelphia, PA 19104-2688 -% USA -% Telephone: (215) 382-9800 -% Fax: (215) 386-7999 -% e-mail: gray@siam.org - -% This is a file of macros and definitions for creating a chapter for -% publication in the SIAM Proceedings series using LaTeX. - -% Report the version. -\message{*** SIAM LaTeX Proceedings Series macro package, version 1.0, -November 6, 1992 ***} - -\pretolerance=800 -\tolerance=10000 -\sloppy - - -\vsize=56pc -\hsize=36pc -\baselineskip=13pt -\hoffset -.5in -\voffset -.5in -\footskip=18pt -\topmargin 24pt -\headheight 12pt -\headsep 15pt -\textheight 53.5pc \advance\textheight by \topskip -\textwidth 36pc -\parskip 0pt -\parindent 18pt -\def\topfraction{.9} -\def\textfraction{.1} -\def\topnumber{2} -%% footnotes to be set 8/10 -\def\footnotesize{\@setsize\footnotesize{11pt}\ixpt\@ixpt - % \indent - \abovedisplayskip \z@ - \belowdisplayskip\z@ - \abovedisplayshortskip\abovedisplayskip - \belowdisplayshortskip\belowdisplayshortskip -\def\@listi{\leftmargin\leftmargini \topsep 3pt plus 1pt minus 1pt - \parsep 2pt plus 1pt minus 1pt - \itemsep \parsep}} - -\let\referencesize\footnotesize - -\footnotesep 0pt - -\skip\footins 12pt plus 12pt - -\def\footnoterule{\kern3\p@ \hrule width 3em\vspace{3pt}} % the \hrule is .4pt high - - -\def\ps@plain{\let\@mkboth\@gobbletwo - \def\@oddfoot{{\hfil\small\thepage\hfil}}% - \def\@oddhead{} - \def\@evenhead{}\def\@evenfoot{}} - - - -\def\ps@headings{\let\@mkboth\markboth - \def\@oddfoot{}\def\@evenfoot{}% - \def\@evenhead{{\rm\thepage}\hspace*{2pc}{\sc\leftmark}\hfil}% - \def\@oddhead{\hfil{\noindent\sc\rightmark}\hspace*{2pc}{\rm\thepage}}% - - - -\def\ps@myheadings{\let\@mkboth\@gobbletwo - \def\@oddfoot{}\def\@evenfoot{}% - \def\@oddhead{\hfil{\sc\rightmark}\hspace*{2pc}{\normalsize\rm\thepage}}% - \def\@evenhead{{\normalsize\rm\thepage}\hspace*{2pc}{\sc\leftmark}\hfil}% -% \def\chaptermark##1{}% - % \def\sectionmark##1{}\def\subsectionmark##1{}} -}} - - - -\def\theequation{\arabic{equation}} - -\def\abstract{\if@twocolumn -\section*{Abstract} -\else \small -\begin{center} -{\bf Abstract\vspace{-.5em}\vspace{3pt}} -\end{center} -\quotation -\fi} -\def\endabstract{\if@twocolumn\else\endquotation\fi} - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% % -% THEOREMS, PROOFS, ALGORITHMS % -% % -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -%%% defined proof environment by theorem model (took out counter) - -\def\qed{{\qquad \vbox{\hrule\hbox{% - \vrule height1.3ex\hskip0.8ex\vrule}\hrule - }}\par} - -\def\newproof#1{\@nprf{#1}} - -\def\@nprf#1#2{\@xnprf{#1}{#2}} - -\def\@xnprf#1#2{\expandafter\@ifdefinable\csname #1\endcsname -\global\@namedef{#1}{\@prf{#1}{#2}}\global\@namedef{end#1}{\@endproof}} - -\def\@prf#1#2{\@xprf{#1}{#2}} - -\def\@xprf#1#2{\@beginproof{#2}{\csname the#1\endcsname}\ignorespaces} - - - -%%% defined algorithm environment by theorem model - -\def\newalgorithm#1{\@ifnextchar[{\@oalg{#1}}{\@nalg{#1}}} - -\def\@nalg#1#2{% -\@ifnextchar[{\@xnalg{#1}{#2}}{\@ynalg{#1}{#2}}} - -\def\@xnalg#1#2[#3]{\expandafter\@ifdefinable\csname #1\endcsname -{\@definecounter{#1}\@addtoreset{#1}{#3}% -\expandafter\xdef\csname the#1\endcsname{\expandafter\noexpand - \csname the#3\endcsname \@thmcountersep \@thmcounter{#1}}% -\global\@namedef{#1}{\@alg{#1}{#2}}\global\@namedef{end#1}{\@endalgorithm}}} - -\def\@ynalg#1#2{\expandafter\@ifdefinable\csname #1\endcsname -{\@definecounter{#1}% -\expandafter\xdef\csname the#1\endcsname{\@thmcounter{#1}}% -\global\@namedef{#1}{\@alg{#1}{#2}}\global\@namedef{end#1}{\@endalgorithm}}} - -\def\@oalg#1[#2]#3{\expandafter\@ifdefinable\csname #1\endcsname - {\global\@namedef{the#1}{\@nameuse{the#2}}% -\global\@namedef{#1}{\@alg{#2}{#3}}% -\global\@namedef{end#1}{\@endalgorithm}}} - -\def\@alg#1#2{\refstepcounter - {#1}\@ifnextchar[{\@yalg{#1}{#2}}{\@xalg{#1}{#2}}} - -\def\@xalg#1#2{\@beginalgorithm{#2}{\csname the#1\endcsname}\ignorespaces} -\def\@yalg#1#2[#3]{\@opargbeginalgorithm{#2}{\csname - the#1\endcsname}{#3}\ignorespaces} - - - - -\def\@beginproof#1{\rm {\it #1.\ }} -\def\@endproof{\outerparskip 0pt\endtrivlist} - -\def\@begintheorem#1#2{\it {\sc #1\ #2.\ }} -\def\@opargbegintheorem#1#2#3{\it - {\sc #1\ #2\ (#3).\ }} -\def\@endtheorem{\outerparskip 0pt\endtrivlist} - -%\def\@begindefinition#1#2{\rm \trivlist \item[\hskip \labelsep{\sc #1\ #2.}]} -%\def\@opargbegindefinition#1#2#3{\rm \trivlist -% \item[\hskip \labelsep{\sc #1\ #2.\ (#3)}]} -%\def\@enddefinition{\outerparskip 0pt\endtrivlist} - - -\def\@beginalgorithm#1#2{\rm \trivlist \item[\hskip \labelsep{\sc #1\ #2.}]} -\def\@opargbeginalgorithm#1#2#3{\rm \trivlist - \item[\hskip \labelsep{\sc #1\ #2.\ (#3)}]} -\def\@endalgorithm{\outerparskip 6pt\endtrivlist} - - -\newskip\outerparskip - -\def\trivlist{\parsep\outerparskip - \@trivlist \labelwidth\z@ \leftmargin\z@ - \itemindent\parindent \def\makelabel##1{##1}} - -\def\@trivlist{\topsep=0pt\@topsepadd\topsep - \if@noskipsec \leavevmode \fi - \ifvmode \advance\@topsepadd\partopsep \else \unskip\par\fi - \if@inlabel \@noparitemtrue \@noparlisttrue - \else \@noparlistfalse \@topsep\@topsepadd \fi - \advance\@topsep \parskip - \leftskip\z@\rightskip\@rightskip \parfillskip\@flushglue - \@setpar{\if@newlist\else{\@@par}\fi}% - \global\@newlisttrue \@outerparskip\parskip} - - -\def\endtrivlist{\if@newlist\@noitemerr\fi - \if@inlabel\indent\fi - \ifhmode\unskip \par\fi - \if@noparlist \else - \ifdim\lastskip >\z@ \@tempskipa\lastskip \vskip -\lastskip - \advance\@tempskipa\parskip \advance\@tempskipa -\@outerparskip - \vskip\@tempskipa - \fi\@endparenv\fi - \vskip\outerparskip} - - - - \newproof{@proof}{Proof} - \newenvironment{proof}{\begin{@proof}}{\end{@proof}} - - \newtheorem{@theorem}{Theorem}[section] - \newenvironment{theorem}{\begin{@theorem}}{\end{@theorem}} - -% \newalgorithm{@algorithm}{Algorithm}[section] -% \newenvironment{algorithm}{\begin{@algorithm}}{\end{@algorithm}} - - - -\newtheorem{lemma}{Lemma}[section] -\newtheorem{fact}{Fact}[section] -\newtheorem{corollary}{Corollary}[section] -\newtheorem{axiom}{Axiom}[section] -\newtheorem{cond}{Condition}[section] -\newtheorem{property}{Property}[section] -\newtheorem{proposition}{Proposition}[section] - -\newtheorem{Conjecture}{Conjecture}[section] -\newtheorem{Definition}{Definition}[section] -\newtheorem{Lemma}{Lemma}[section] -\newtheorem{Remark}{Remark}[section] - -\newproof{Example}{Example} -\newproof{Method}{Method} -\newproof{Exercise}{Exercise} - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% % -% TABLE AND FIGURE CAPTIONS % -% % -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - \def\@figtxt{figure} -\long\def\@makecaption#1#2{\small -\setlength{\parindent}{18pt} -\baselineskip 14pt - \ifx\@captype\@figtxt - \vskip 10pt - \setbox\@tempboxa\hbox{{\sc #1} {\it #2}} - \ifdim \wd\@tempboxa >\hsize {\sc #1} {\it #2}\par \else \hbox -to\hsize{\hfil\box\@tempboxa\hfil}% - \fi\else\hbox to\hsize{\hfil{\sc #1}\hfil}% - \setbox\@tempboxa\hbox{{\it #2}}% - \ifdim \wd\@tempboxa >\hsize {\it #2}\par \else - \hbox to \hsize{\hfil\box\@tempboxa\hfil}\fi - \vskip 10pt - \fi} - - -%\newif\iftable \global\tablefalse - - -%\long\def\@makecaption#1#2{% -%\setlength{\parindent}{18pt} -% \vskip 12pt -% \iftable - % \hbox to \hsize{\hfil\sc #1\hfil} - % \hbox to \hsize{\hfil\it #2\hfil} - % \global\tablefalse - % \else - % \setbox\@tempboxa\hbox{{\small#1} {\small\it#2}} - % \ifdim \wd\@tempboxa >\hsize - % \indent{\small#1}{\small\it#2}\par - % \else - % \hbox to\hsize{\hfil\box\@tempboxa\hfil}\fi - % \fi} -% \vskip 6pt} - - - -%\def\figure{\global\tablefalse\@float{figure}} -\def\fnum@figure{\par\sc Fig. \thefigure.\ } -%\def\fnum@figure{\par\sc Fig. \thefigure\ } - -%\def\table{\global\tabletrue\@float{table}} -\def\fnum@table{\small \sc Table \thetable} - - - - - - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% % -% SECTIONS % -% % -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -\def\section{\@startsection {section}{1}{\z@}{-3.5ex plus -1ex minus - -.2ex}%{2.3ex plus .2ex} -{2pt}{\large\bf}} -\def\subsection{\@startsection{subsection}{2}{\z@}{-3.25ex plus -1ex minus - -.2ex}%{1.5ex plus .2ex} -{2pt}{\large\bf}} -\def\subsubsection{\@startsection {subsubsection}{3}{\z@}{1.3ex plus .5ex minus - .2ex}{-.5em plus -.1em}{\normalsize\bf}} - - - - - - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% %% -%% BIBLIOGRAPHY %% -%% %% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - - -\def\thebibliography#1{% -%\cleardoublepage -\parindent 0em -\vspace{9pt} -\begin{flushleft}\large\bf {References}\end{flushleft} -\addvspace{3pt}\nopagebreak\list - %% default is no labels, for those not using \cite or BibTeX -{[\arabic{enumi}]} {\settowidth\labelwidth{[#1]} -%%{[\arabic{enumi}]}{\settowidth\labelwidth{mm} -\leftmargin\labelwidth -\leftmargin=17pt - \advance\leftmargin\labelsep - \usecounter{enumi}\@bibsetup} -\def\newblock{\hskip .11em plus .33em minus -.07em} - \sloppy\clubpenalty4000\widowpenalty4000 - \sfcode`\.=1000\relax} - - - -%% setup 8/10 type -\def\@bibsetup{%\itemindent=0pt -\itemsep=0pt \parsep=0pt -\small} - -\def\sameauthor{\leavevmode\vrule height 2pt depth -1.6pt width 23pt} - - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% % -% INDEX % -% % -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - - -%makeindex.sty official version 6.4 -%The second line came from /usr/misc/lib/tex82/report.sty. - -\def\theindex{\@restonecoltrue\if@twocolumn\@restonecolfalse\fi -\columnseprule \z@ -\columnsep 35pt\twocolumn[\chapter*{Index}] - \parskip\z@ plus .3pt\relax\let\item\@idxitem} - - -\def\printindex{\cleardoublepage\markboth{INDEX}{INDEX} -\addcontentsline{toc}{chapter}{Index}\@input{\jobname.ind}} - -\ps@headings - - -%%% end of style file - -%%%%%%%%%%%%%%%%%%%%%%%%%%CUT HERE%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -% This is siamproc.bst -% SIAM bibliography style (29-Jan-88 version) -% numeric labels, alphabetic order, Mathematical Reviews abbreviations, -% names in \sc, titles in italics, book titles mixed upper-lower and article -% titles lowercase, commas separate all fields except before "notes". -% -% History -% 1/30/86 (HWT) Original version, by Howard Trickey. -% 6/15/87 (HWT) Fix format.editors---Martin Costabel. -% 1/29/88 (OP&HWT) Updated for BibTeX version 0.99a, Oren Patashnik; -% THIS `siam' VERSION DOES NOT WORK WITH BIBTEX 0.98i. - -ENTRY - { address - author - booktitle - chapter - edition - editor - howpublished - institution - journal - key - month - note - number - organization - pages - publisher - school - series - title - type - volume - year - } - {} - { label } - -INTEGERS { output.state before.all mid.sentence after.block } - -FUNCTION {init.state.consts} -{ #0 'before.all := - #1 'mid.sentence := - #2 'after.block := -} - -STRINGS { s t } - -FUNCTION {output.nonnull} -{ 's := - output.state mid.sentence = - { ", " * write$ } - { output.state after.block = - { add.period$ write$ - newline$ - "\newblock " write$ - } - 'write$ - if$ - mid.sentence 'output.state := - } - if$ - s -} - -FUNCTION {output} -{ duplicate$ empty$ - 'pop$ - 'output.nonnull - if$ -} - -FUNCTION {output.check} -{ 't := - duplicate$ empty$ - { pop$ "empty " t * " in " * cite$ * warning$ } - 'output.nonnull - if$ -} - -FUNCTION {output.bibitem} -{ newline$ - "\bibitem{" write$ - cite$ write$ - "}" write$ - newline$ - "" - before.all 'output.state := -} - -FUNCTION {fin.entry} -{ add.period$ - write$ - newline$ -} - -FUNCTION {new.block} -{ output.state before.all = - 'skip$ - { after.block 'output.state := } - if$ -} - -FUNCTION {not} -{ { #0 } - { #1 } - if$ -} - -FUNCTION {and} -{ 'skip$ - { pop$ #0 } - if$ -} - -FUNCTION {or} -{ { pop$ #1 } - 'skip$ - if$ -} - -FUNCTION {new.block.checka} -{ empty$ - 'skip$ - 'new.block - if$ -} - -FUNCTION {field.or.null} -{ duplicate$ empty$ - { pop$ "" } - 'skip$ - if$ -} - -FUNCTION {emphasize} -{ duplicate$ empty$ - { pop$ "" } - { "{\em " swap$ * "}" * } - if$ -} - -FUNCTION {scapify} -{ duplicate$ empty$ - { pop$ "" } - { "{\sc " swap$ * "}" * } - if$ -} - -INTEGERS { nameptr namesleft numnames } - -FUNCTION {format.names} -{ 's := - #1 'nameptr := - s num.names$ 'numnames := - numnames 'namesleft := - { namesleft #0 > } - { s nameptr "{f.~}{vv~}{ll}{, jj}" format.name$ 't := - nameptr #1 > - { namesleft #1 > - { ", " * t * } - { numnames #2 > - { "," * } - 'skip$ - if$ - t "others" = - { " et~al." * } - { " and " * t * } - if$ - } - if$ - } - 't - if$ - nameptr #1 + 'nameptr := - namesleft #1 - 'namesleft := - } - while$ -} - -STRINGS { last.authors } - -FUNCTION {init.last.authors} -{ "" 'last.authors := -} - -FUNCTION {format.authors} -{ author empty$ - { "" 'last.authors := - "" - } - { author last.authors = - { "\leavevmode\vrule height 2pt depth -1.6pt width 23pt" } - { author format.names }% scapify } - if$ - author 'last.authors := - } - if$ -} - -FUNCTION {format.organization} -{ organization empty$ - { "" 'last.authors := - "" - } - { organization last.authors = - { "\leavevmode\vrule height 2pt depth -1.6pt width 23pt" } - { organization scapify } - if$ - organization 'last.authors := - } - if$ -} - -FUNCTION {format.editors} -{ editor empty$ - { "" 'last.authors := - "" - } - { editor last.authors = - { "\leavevmode\vrule height 2pt depth -1.6pt width 23pt" } - { editor format.names scapify } - if$ - editor num.names$ #1 > - { ", eds." * } - { ", ed." * } - if$ - editor 'last.authors := - } - if$ -} - -FUNCTION {format.ineditors} -{ editor empty$ - { "" } - { editor format.names - editor num.names$ #1 > - { ", eds." * } - { ", ed." * } - if$ - } - if$ -} - -FUNCTION {format.title} -{ title empty$ - { "" } - { title "t" change.case$ emphasize } - if$ -} - -FUNCTION {n.dashify} -{ 't := - "" - { t empty$ not } - { t #1 #1 substring$ "-" = - { t #1 #2 substring$ "--" = not - { "--" * - t #2 global.max$ substring$ 't := - } - { { t #1 #1 substring$ "-" = } - { "-" * - t #2 global.max$ substring$ 't := - } - while$ - } - if$ - } - { t #1 #1 substring$ * - t #2 global.max$ substring$ 't := - } - if$ - } - while$ -} - -FUNCTION {format.date} -{ year empty$ - { month empty$ - { "" } - { "there's a month but no year in " cite$ * warning$ - month - } - if$ - } - { month empty$ - 'year - { month " " * year * } - if$ - } - if$ -} - -FUNCTION {format.btitle} -{ title emphasize -} - -FUNCTION {tie.or.space.connect} -{ duplicate$ text.length$ #3 < - { "~" } - { " " } - if$ - swap$ * * -} - -FUNCTION {either.or.check} -{ empty$ - 'pop$ - { "can't use both " swap$ * " fields in " * cite$ * warning$ } - if$ -} - -FUNCTION {format.bvolume} -{ volume empty$ - { "" } - { "vol.~" volume * - series empty$ - 'skip$ - { " of " * series * } - if$ - "volume and number" number either.or.check - } - if$ -} - -FUNCTION {format.number.series} -{ volume empty$ - { number empty$ - { series field.or.null } - { "no.~" number * - series empty$ - { "there's a number but no series in " cite$ * warning$ } - { " in " * series * } - if$ - } - if$ - } - { "" } - if$ -} - -FUNCTION {format.edition} -{ edition empty$ - { "" } - { edition "l" change.case$ "~ed." * } - if$ -} - -INTEGERS { multiresult } - -FUNCTION {multi.page.check} -{ 't := - #0 'multiresult := - { multiresult not - t empty$ not - and - } - { t #1 #1 substring$ - duplicate$ "-" = - swap$ duplicate$ "," = - swap$ "+" = - or or - { #1 'multiresult := } - { t #2 global.max$ substring$ 't := } - if$ - } - while$ - multiresult -} - -FUNCTION {format.pages} -{ pages empty$ - { "" } - { pages multi.page.check - { "pp.~" pages n.dashify * } - { "p.~" pages * } - if$ - } - if$ -} - -FUNCTION {format.vol.year} -{ volume field.or.null - year empty$ - { "empty year in " cite$ * warning$ } - { " (" year * ")" * * } - if$ -} - -FUNCTION {format.chapter.pages} -{ chapter empty$ - 'format.pages - { type empty$ - { "ch.~" chapter * } - { type "l" change.case$ chapter tie.or.space.connect } - if$ - pages empty$ - 'skip$ - { ", " * format.pages * } - if$ - } - if$ -} - -FUNCTION {format.in.ed.booktitle} -{ booktitle empty$ - { "" } - { editor empty$ - { "in " booktitle * } - { "in " booktitle * ", " * format.ineditors * } - if$ - } - if$ -} - -FUNCTION {empty.misc.check} -{ author empty$ title empty$ howpublished empty$ - month empty$ year empty$ note empty$ - and and and and and - key empty$ not and - { "all relevant fields are empty in " cite$ * warning$ } - 'skip$ - if$ -} - -FUNCTION {format.thesis.type} -{ type empty$ - 'skip$ - { pop$ - type "l" change.case$ - } - if$ -} - -FUNCTION {format.tr.number} -{ type empty$ - { "Tech. Rep." } - 'type - if$ - number empty$ - { "l" change.case$ } - { number tie.or.space.connect } - if$ -} - -FUNCTION {format.article.crossref} -{ key empty$ - { journal empty$ - { "need key or journal for " cite$ * " to crossref " * crossref * - warning$ - "" - } - { "in " journal * } - if$ - } - { "in " key * } - if$ - " \cite{" * crossref * "}" * -} - -FUNCTION {format.crossref.editor} -{ editor #1 "{vv~}{ll}" format.name$ - editor num.names$ duplicate$ - #2 > - { pop$ " et~al." * } - { #2 < - 'skip$ - { editor #2 "{ff }{vv }{ll}{ jj}" format.name$ "others" = - { " et~al." * } - { " and " * editor #2 "{vv~}{ll}" format.name$ * } - if$ - } - if$ - } - if$ -} - -FUNCTION {format.book.crossref} -{ volume empty$ - { "empty volume in " cite$ * "'s crossref of " * crossref * warning$ - "in " - } - { "vol.~" volume * - " of " * - } - if$ - editor empty$ - editor field.or.null author field.or.null = - or - { key empty$ - { series empty$ - { "need editor, key, or series for " cite$ * " to crossref " * - crossref * warning$ - "" * - } - { series * } - if$ - } - { key * } - if$ - } - { format.crossref.editor * } - if$ - " \cite{" * crossref * "}" * -} - -FUNCTION {format.incoll.inproc.crossref} -{ editor empty$ - editor field.or.null author field.or.null = - or - { key empty$ - { booktitle empty$ - { "need editor, key, or booktitle for " cite$ * " to crossref " * - crossref * warning$ - "" - } - { "in " booktitle * } - if$ - } - { "in " key * } - if$ - } - { "in " format.crossref.editor * } - if$ - " \cite{" * crossref * "}" * -} - -FUNCTION {article} -{ output.bibitem - format.authors "author" output.check - format.title "title" output.check - crossref missing$ - { journal "journal" output.check - format.vol.year output - } - { format.article.crossref output.nonnull } - if$ - format.pages output - new.block - note output - fin.entry -} - -FUNCTION {book} -{ output.bibitem - author empty$ - { format.editors "author and editor" output.check } - { format.authors output.nonnull - crossref missing$ - { "author and editor" editor either.or.check } - 'skip$ - if$ - } - if$ - format.btitle "title" output.check - crossref missing$ - { format.bvolume output - format.number.series output - publisher "publisher" output.check - address output - } - { format.book.crossref output.nonnull } - if$ - format.edition output - format.date "year" output.check - new.block - note output - fin.entry -} - -FUNCTION {booklet} -{ output.bibitem - format.authors output - format.title "title" output.check - howpublished new.block.checka - howpublished output - address output - format.date output - new.block - note output - fin.entry -} - -FUNCTION {inbook} -{ output.bibitem - author empty$ - { format.editors "author and editor" output.check } - { format.authors output.nonnull - crossref missing$ - { "author and editor" editor either.or.check } - 'skip$ - if$ - } - if$ - format.btitle "title" output.check - crossref missing$ - { format.bvolume output - format.number.series output - publisher "publisher" output.check - address output - } - { format.book.crossref output.nonnull } - if$ - format.edition output - format.date "year" output.check - format.chapter.pages "chapter and pages" output.check - new.block - note output - fin.entry -} - -FUNCTION {incollection} -{ output.bibitem - format.authors "author" output.check - format.title "title" output.check - crossref missing$ - { format.in.ed.booktitle "booktitle" output.check - format.bvolume output - format.number.series output - publisher "publisher" output.check - address output - format.edition output - format.date "year" output.check - } - { format.incoll.inproc.crossref output.nonnull } - if$ - format.chapter.pages output - new.block - note output - fin.entry -} - -FUNCTION {inproceedings} -{ output.bibitem - format.authors "author" output.check - format.title "title" output.check - crossref missing$ - { format.in.ed.booktitle "booktitle" output.check - format.bvolume output - format.number.series output - address empty$ - { organization output - publisher output - format.date "year" output.check - } - { address output.nonnull - format.date "year" output.check - organization output - publisher output - } - if$ - } - { format.incoll.inproc.crossref output.nonnull } - if$ - format.pages output - new.block - note output - fin.entry -} - -FUNCTION {conference} { inproceedings } - -FUNCTION {manual} -{ output.bibitem - author empty$ - { format.organization output } - { format.authors output.nonnull } - if$ - format.btitle "title" output.check - author empty$ - 'skip$ - { organization output } - if$ - address output - format.edition output - format.date output - new.block - note output - fin.entry -} - -FUNCTION {mastersthesis} -{ output.bibitem - format.authors "author" output.check - format.title "title" output.check - "Master's thesis" format.thesis.type output.nonnull - school "school" output.check - address output - format.date "year" output.check - new.block - note output - fin.entry -} - -FUNCTION {misc} -{ output.bibitem - format.authors output - format.title output - howpublished new.block.checka - howpublished output - format.date output - new.block - note output - fin.entry - empty.misc.check -} - -FUNCTION {phdthesis} -{ output.bibitem - format.authors "author" output.check - format.btitle "title" output.check - "PhD thesis" format.thesis.type output.nonnull - school "school" output.check - address output - format.date "year" output.check - new.block - note output - fin.entry -} - -FUNCTION {proceedings} -{ output.bibitem - editor empty$ - { format.organization output } - { format.editors output.nonnull } - if$ - format.btitle "title" output.check - format.bvolume output - format.number.series output - address empty$ - { editor empty$ - 'skip$ - { organization output } - if$ - publisher output - format.date "year" output.check - } - { address output.nonnull - format.date "year" output.check - editor empty$ - 'skip$ - { organization output } - if$ - publisher output - } - if$ - new.block - note output - fin.entry -} - -FUNCTION {techreport} -{ output.bibitem - format.authors "author" output.check - format.title "title" output.check - format.tr.number output.nonnull - institution "institution" output.check - address output - format.date "year" output.check - new.block - note output - fin.entry -} - -FUNCTION {unpublished} -{ output.bibitem - format.authors "author" output.check - format.title "title" output.check - new.block - note "note" output.check - format.date output - fin.entry -} - -FUNCTION {default.type} { misc } - -MACRO {jan} {"Jan."} - -MACRO {feb} {"Feb."} - -MACRO {mar} {"Mar."} - -MACRO {apr} {"Apr."} - -MACRO {may} {"May"} - -MACRO {jun} {"June"} - -MACRO {jul} {"July"} - -MACRO {aug} {"Aug."} - -MACRO {sep} {"Sept."} - -MACRO {oct} {"Oct."} - -MACRO {nov} {"Nov."} - -MACRO {dec} {"Dec."} - -MACRO {acmcs} {"ACM Comput. Surveys"} - -MACRO {acta} {"Acta Inf."} - -MACRO {cacm} {"Comm. ACM"} - -MACRO {ibmjrd} {"IBM J. Res. Dev."} - -MACRO {ibmsj} {"IBM Syst.~J."} - -MACRO {ieeese} {"IEEE Trans. Softw. Eng."} - -MACRO {ieeetc} {"IEEE Trans. Comput."} - -MACRO {ieeetcad} - {"IEEE Trans. Comput.-Aided Design Integrated Circuits"} - -MACRO {ipl} {"Inf. Process. Lett."} - -MACRO {jacm} {"J.~Assoc. Comput. Mach."} - -MACRO {jcss} {"J.~Comput. System Sci."} - -MACRO {scp} {"Sci. Comput. Programming"} - -MACRO {sicomp} {"SIAM J. Comput."} - -MACRO {tocs} {"ACM Trans. Comput. Syst."} - -MACRO {tods} {"ACM Trans. Database Syst."} - -MACRO {tog} {"ACM Trans. Gr."} - -MACRO {toms} {"ACM Trans. Math. Softw."} - -MACRO {toois} {"ACM Trans. Office Inf. Syst."} - -MACRO {toplas} {"ACM Trans. Prog. Lang. Syst."} - -MACRO {tcs} {"Theoretical Comput. Sci."} - -READ - -FUNCTION {sortify} -{ purify$ - "l" change.case$ -} - -INTEGERS { len } - -FUNCTION {chop.word} -{ 's := - 'len := - s #1 len substring$ = - { s len #1 + global.max$ substring$ } - 's - if$ -} - -FUNCTION {sort.format.names} -{ 's := - #1 'nameptr := - "" - s num.names$ 'numnames := - numnames 'namesleft := - { namesleft #0 > } - { nameptr #1 > - { " " * } - 'skip$ - if$ - s nameptr "{vv{ } }{ll{ }}{ f{ }}{ jj{ }}" format.name$ 't := - nameptr numnames = t "others" = and - { "et al" * } - { t sortify * } - if$ - nameptr #1 + 'nameptr := - namesleft #1 - 'namesleft := - } - while$ -} - -FUNCTION {sort.format.title} -{ 't := - "A " #2 - "An " #3 - "The " #4 t chop.word - chop.word - chop.word - sortify - #1 global.max$ substring$ -} - -FUNCTION {author.sort} -{ author empty$ - { key empty$ - { "to sort, need author or key in " cite$ * warning$ - "" - } - { key sortify } - if$ - } - { author sort.format.names } - if$ -} - -FUNCTION {author.editor.sort} -{ author empty$ - { editor empty$ - { key empty$ - { "to sort, need author, editor, or key in " cite$ * warning$ - "" - } - { key sortify } - if$ - } - { editor sort.format.names } - if$ - } - { author sort.format.names } - if$ -} - -FUNCTION {author.organization.sort} -{ author empty$ - { organization empty$ - { key empty$ - { "to sort, need author, organization, or key in " cite$ * warning$ - "" - } - { key sortify } - if$ - } - { "The " #4 organization chop.word sortify } - if$ - } - { author sort.format.names } - if$ -} - -FUNCTION {editor.organization.sort} -{ editor empty$ - { organization empty$ - { key empty$ - { "to sort, need editor, organization, or key in " cite$ * warning$ - "" - } - { key sortify } - if$ - } - { "The " #4 organization chop.word sortify } - if$ - } - { editor sort.format.names } - if$ -} - -FUNCTION {presort} -{ type$ "book" = - type$ "inbook" = - or - 'author.editor.sort - { type$ "proceedings" = - 'editor.organization.sort - { type$ "manual" = - 'author.organization.sort - 'author.sort - if$ - } - if$ - } - if$ - " " - * - year field.or.null sortify - * - " " - * - title field.or.null - sort.format.title - * - #1 entry.max$ substring$ - 'sort.key$ := -} - -ITERATE {presort} - -SORT - -STRINGS { longest.label } - -INTEGERS { number.label longest.label.width } - -FUNCTION {initialize.longest.label} -{ "" 'longest.label := - #1 'number.label := - #0 'longest.label.width := -} - -FUNCTION {longest.label.pass} -{ number.label int.to.str$ 'label := - number.label #1 + 'number.label := - label width$ longest.label.width > - { label 'longest.label := - label width$ 'longest.label.width := - } - 'skip$ - if$ -} - -EXECUTE {initialize.longest.label} - -ITERATE {longest.label.pass} - -FUNCTION {begin.bib} -{ preamble$ empty$ - 'skip$ - { preamble$ write$ newline$ } - if$ - "\begin{thebibliography}{" longest.label * "}" * write$ newline$ -} - -EXECUTE {begin.bib} - -EXECUTE {init.state.consts} - -EXECUTE {init.last.authors} - -ITERATE {call.type$} - -FUNCTION {end.bib} -{ newline$ - "\end{thebibliography}" write$ newline$ -} - -EXECUTE {end.bib} - diff --git a/Master/texmf-dist/source/latex/siam/ptexconf.all b/Master/texmf-dist/source/latex/siam/ptexconf.all deleted file mode 100644 index 06e2a7f38ae..00000000000 --- a/Master/texmf-dist/source/latex/siam/ptexconf.all +++ /dev/null @@ -1,102 +0,0 @@ - -Please answer the following: - -1. Name of conference -2. Type of Presentation - Contributed: Lecture form or Poster form - Minisymposium: - -3. Equipment for Visual Support - Lecture form/Minisymposium: Overhead Projector or - 2" x 2" Slide Projector (35mm) - - Poster form: Easel or Poster Board - -4. If you are a speaker in a minisymposium, who is the organizer? - -5. What is the minisymposium title? - -6. If more than one author, who will present the paper? - - -%This is a macro file for creating a SIAM Conference abstract in -% Plain Tex. -% -% If you have any questions regarding these macros contact: -% Lillian Hunt -% SIAM -% 3600 University City Center Center -% Philadelphia, PA 19104-2688 -% USA -% (215) 382-9800 -% e-mail:meetings@siam.org - - -\hsize=25.5pc -\vsize=50pc -\parskip=3pt -\parindent=0pt -\overfullrule=0pt -\nopagenumbers - -\def\title#1\\{\bf{#1}\vskip6pt} -\def\abstract#1\\{\rm {#1}} -\def\author#1\\{\vskip6pt\rm {#1}\vfill\eject} -\def\eol{\hfill\break} - -% end of style file - -% This is ptexconf.tex. Use this file as an example of a SIAM -% Conference abstract in plain TeX. - -\input ptexconf.sty - -\title Numerical Analysis of a 1-Dimensional -Immersed-Boundary Method\\ - -\abstract We present the numerical analysis of a simplified, -one-dimensional version -of Peskin's immersed boundary method, which has been used to -solve -the two- and three-dimensional Navier-Stokes equations in the -presence of immersed boundaries. We consider the heat -equation - in a finite domain with a moving source term. -We denote the solution as $u(x,t)$ and the location of the -source - term as $X(t)$. The source term is a moving delta function -whose strength is a function of u at the location of the -delta function. -The p.d.e. is coupled to an ordinary differential equation -whose -solution gives the location of the source term. - The o.d.e. is $X'(t) = u(X(t),t)$, which can be interpreted as -saying the source term moves at the local velocity. -The accuracy the numerical method of solution depends on how -the -delta function is discretized when the delta function is not -at -a grid point and on how the solution, u, is represented - at locations between grid points. We present results showing -the effect of different choices of spreading the source to -the grid and -of restricting the solution to the source location. -The problem we analyze is also similar to the Stefan problem -and -the immersed-boundary method has features in common with -particle-in-cell - methods.\\ - \author\underbar{Richard P. Beyer, Jr.}\eol -University of Washington, Seattle, WA\eol -%\vskip3pt -Randall J. LeVeque\eol -University of Washington, Seattle, WA\\ -\bye - -% end of example file - - -Please furnish complete addresses for all co-authors. - - -PLEASE BE SURE TO INDICATE WHAT CONFERENCE THE ABSTRACT IS FOR.
\ No newline at end of file diff --git a/Master/texmf-dist/source/latex/siam/ptexnec.all b/Master/texmf-dist/source/latex/siam/ptexnec.all deleted file mode 100644 index 2da4cfce16f..00000000000 --- a/Master/texmf-dist/source/latex/siam/ptexnec.all +++ /dev/null @@ -1,707 +0,0 @@ - - -This file (ptexnec.all) constitutes the full distribution of NEC Proceedings Series -Plain TeX macros. The files are: - -ptexnec.tex (An example file, also containing documentation) - -ptexnec.sty (the style file) - -To use these macros, separate at the indicated cut lines. - -%%%%%%%%%%%%%%%%%%%%%%%%%CUT HERE%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -% This is ptexnec.tex, an example file for use with the NEC Plain TeX -% Proceedings Series macros. Comments are placed at the beginning and -% throughout this file. Please take the time to read them as they document -% how to use these macros. This file can be composed and printed out for -% use as sample output. Please ignore the underfull \vbox on page 3. - -% Any comments or questions regarding these macros should be directed to: -% -% Corey Gray -% SIAM -% 3600 University City Science Center -% Philadelphia, PA 19104-2688 -% USA -% Telephone: (215) 382-9800 -% Fax: (215) 386-7999 -% e-mail: gray@siam.org - - -% This file is to be used as an example for style only. It should not be read -% for content. - -%%%%%%%%%%%%%%% PLEASE NOTE THE FOLLOWING STYLE RESTRICTIONS %%%%%%%%%%%%%%% - -%% 1. You must use the numbered reference style([1],[2]), listing the -%% references at the end of the chapter either by order of citation -%% or alphabetically. -%% -%% 2. This macro is set up for three levels of headings. Use the commands -%% \headone, \headtwo, and \headthree. The macro will automatically -%% number the headings. -%% -%% 3. The running heads are defined by the commands \def\leftrh{} and -%% \def\rightrh{}. You must fill in the empty field of these commands -%% with the appropriate information. The left running head should be the -%% authors names. For papers with multiple authors, please follow these -%% rules; for two authors type {Author 1 and Author 2}; for more than two -%% authors type {Author 1 et al.}. The right running head is the title of -%% the paper. If the title is more than 50 characters, including spaces, -%% please provide a shortened version. All information should be typed -%% initial cap and lower case. -%% -%% 5. Theorems, Lemmas, Definitions, etc. are to be double-numbered, -%% indicating the section and the occurrence of that element -%% within that section. (For example, the first theorem in the second -%% section would be numbered 2.1.) This numbering must -%% be done manually. -%% -%% 6. Proofs are handled by \prf\endprf. If you want to use an end-of-proof -%% box, insert \qed right before the \endprf command. -%% -%% 7. Figures and equations must be manually single-numbered. Use \leqno -%% for equation numbering. The macro provides the \fig for including -%% figures. This command consists of three fields. The first field is -%% used for inserting the appropriate space for the figure. The second -%% field is the figure number. The third field is the caption. See the -%% example included in this file. SIAM supports the use of psfig for -%% including Postscript figures. All Postscript figures should be sent -%% as separate files. A hardcopy version of all Postscript figures is -%% also required. See note regarding this under How to Submit Your Paper. -%% -%% 8. Use of \title\endtitle and \lasttitle\endlastitle. -%% This macro package provides two possible commands for handling the -%% title of your paper. The commands \title\endtitle should be used for -%% all lines except the last line of multiple line titles. The commands -%% \lasttitle\endlasttitle should be used for the last line of multiple -%% line titles. In the case of a single line title, \lasttitle\endlasttitle -%% should be used. -%% -%% 9. Use of \author\endauthor and \lastauthor\endlastauthor. -%% As in the title macro, two possible commands are provided for the -%% author. The commands \author\endauthor should be used for the first -%% line of authors if there are more than one line. The commands -%% \lastauthor\endlastauthor should be used for the last line -%% of multiple lines of authors. In the case of a single line of authors, -%% \lastauthor\endlastauthor should be used. A maximum of four authors -%% should be placed on any one line. The appropriate space must also be -%% hard coded between authors on the same line. The spacing is as follows: -%% -%% If 2 authors; \hskip4pc between -%% If 3 authors; \hskip3pc between -%% If 4 authors; \hskip2pc between -%% -%% 10. Grant information and author affiliations. -%% This information is included by using the \footnote command and the -%% appropriate footnote symbol. SIAM uses footnote symbols in a -%% particular order. Below is a list of these symbols: -%% -%% asterisk -%% single-dagger -%% double-dagger -%% section sign -%% paragraph -%% parallel -%% double asterisk -%% double single-dagger -%% double double-dagger -%% -%% For illustrative purposes, all footnote symbols have been used in the -%% example file. -%% -%% A note regarding \footnote. This command seems to leave extra white -%% space between footnotes. This is quite evident in the example file. If -%% any user of these macros has a solution to this problem, I would -%% appreciate hearing from you. Send your comments to: gray@siam.org. -%% -%% The following general rules apply for including grants and affiliations: -%% a) If there is a single grant for the paper, then the grant -%% information should be footnoted to the title. -%% b) If there is more than one grant, included the grant information -%% with each authors affiliation. -%% c) If there are different grants for the paper but the authors share -%% the same affiliation, footnote the grant information to the title. -%% For example, The work of the first author was supported by xyz. -%% The work of the second author was supported by abc. And so on. -%% -%% -%% 11. Special fonts. -%% SIAM supports the use of AMS-TeX fonts version 2.0 and later. As -%% described in the manual for these fonts, they can be included by -%% \input{amssym.def} and \input{amssym.tex}. -%% -%% 12. How to Submit Your Paper. -%% The electronic version of your paper should be sent to proceed@siam.org. -%% A hardcopy version should also be submitted. Instructions are included -%% in your acceptance letter. Please be sure to send hardcopy -%% versions of any Postscript figures you have submitted electronically. -%% Be sure to return your signed Copyright Transfer Agreement. We cannot -%% publish your paper without one.%% -%% -%% - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -\input ptexnec.sty - -\def\leftrh{Gray et al.} -\def\rightrh{NEC Proceedings Series Macros} - -\startchapter %Place this command at the beginning of the file immediately - %after the \input command. - - - -\title Chapter 1\endtitle -\title NEC Proceedings Series Macros\endtitle -\lasttitle for Use with Plain TeX\footnote*{Any information -regarding grants should be placed here.}\endlasttitle - -\author J. Corey Gray\footnote{$^{\dag}$}{Production Manager, Society for -Industrial and Applied Mathematics, Philadelphia, PA.} -\hskip2truepc Tricia Manning\footnote{$^{\ddag}$}{Publications -Specialist, Society for Industrial and Applied Mathematics, Philadelphia, -PA.} -\hskip2truepc Vickie Kearn\footnote{$^{\S}$}{Publisher, Society for Industrial -and Applied Mathematics, Philadelphia, PA.} -\hskip2truepc Nancy Abbott\footnote{$^{\P}$}{Design Supervisor, Society for -Industrial and Applied Mathematics, Philadelphia, PA.} -\endauthor -\lastauthor Sue Ciambrano\footnote{$^{\parallel}$}{Acquisition Editor, Society for -Industrial and Applied Mathematics, Philadelphia, PA.} -\hskip2truepc Paul Duggan\footnote{$^{**}$}{Composition -Specialist, Society for Industrial and Applied Mathematics, Philadelphia, -PA.} -\hskip2truepc Robbi Anne Albert\footnote{$^{\dagger\dagger}$}{Production, -Assistant, Society for Industrial -and Applied Mathematics, Philadelphia, PA.} -\hskip2truepc Jean Anderson\footnote{$^{\ddag\ddag}$}{Composition Coordinator, Society for -Industrial and Applied Mathematics, Philadelphia, PA.} -\endlastauthor - -% Use \headone for the first level headings. The macro will automatically -% number the headings. - -\centerline{\bf Abstract} -\abstract An equivalence is shown between realizability of input/output (i/o) operators by -rational control systems and high-order algebraic differential equations for -i/o pairs. This generalizes, to nonlinear systems, the equivalence -between autoregressive representations and finite dimensional linear -realizability.\endabstract - - -\headone{Problem Specification} -In this paper, we consider the solution of the $N \times N$ linear -system -$$A x = b\leqno (1)$$ -where $A$ is large, sparse, symmetric, and positive definite. We consider -the direct solution of by means of general sparse Gaussian -elimination. In such a procedure, we find a permutation matrix $P$, and -compute the decomposition -$$ -P A P^{t} = L D L^{t} -\leqno (2)$$ - -\noindent where $L$ is unit lower triangular and $D$ is diagonal. - - -\headone{Design Considerations} -Several good ordering algorithms (nested dissection and minimum degree) -are available for computing $P$ [1], [2]. -Since our interest here does not -focus directly on the ordering, we assume for convenience that $P=I$, -or that $A$ has been preordered to reflect an appropriate choice of $P$. - -% Use \thm and \endthm for theorems. They must be numbered manually. -% Lemmas (\lem \endlem), corollaries (\cor \endcor), and -% propositions (\prop \endprop) are coded the same as theorems and must -% also be numbered manually. - -\thm{Theorem 2.1.} The method was extended to three -dimensions. For the standard multigrid -coarsening -(in which, for a given grid, the next coarser grid has $1/8$ -as many points), anisotropic problems require plane -relaxation to -obtain a good smoothing factor.\endthm - -Several good ordering algorithms (nested dissection and minimum degree) -are available for computing $P$ [1], [2]. -Since our interest here does not -focus directly on the ordering, we assume for convenience that $P=I$, -or that $A$ has been preordered to reflect an appropriate choice of $P$. -Several good ordering algorithms (nested dissection and minimum degree) -are available for computing $P$ [1], [2]. -Since our interest here does not -focus directly on the ordering, we assume for convenience that $P=I$, -or that $A$ has been preordered to reflect an appropriate choice of $P$. - -% Use \prf and \endprf to begin and end a proof. -% The use of \qed will produce an end-of-proof box. - -\prf{Proof} In this paper we consider two methods. The first method -is -basically the method considered with two differences: -first, we perform plane relaxation by a two-dimensional -multigrid method, and second, we use a slightly different -choice of -interpolation operator, which improves performance -for nearly singular problems. In the second method coarsening -is done by successively coarsening each.\qed\endprf - -% Use \dfn and \enddfn to begin and end definitions. - -\dfn{Definition 2.1.}We describe the two methods in \S\ 1.2. This is a -definition in the plain tex macro.\enddfn - -This is accomplished by exploiting the m-tree, -a particular spanning tree for the graph of the filled-in matrix. -Our purpose here is to examine the nonnumerical complexity of the -sparse elimination algorithm given in [3]. -As was shown there, a general sparse elimination scheme based on the -bordering algorithm requires less storage for pointers and -row/column indices than more traditional implementations of general -sparse elimination. This is accomplished by exploiting the m-tree, -a particular spanning tree for the graph of the filled-in matrix. - - -Our purpose here is to examine the nonnumerical complexity of the -sparse elimination algorithm given in [3]. -As was shown there, a general sparse elimination scheme based on the -bordering algorithm requires less storage for pointers and -row/column indices than more traditional implementations of general -sparse elimination. This is accomplished by exploiting the m-tree, -a particular spanning tree for the graph of the filled-in matrix. -Since our interest here does not -focus directly on the ordering, we assume for convenience that $P=I$, -or that $A$ has been preordered to reflect an appropriate choice of $P$. - -% Use \lem and \endlem to begin and end lemmas. - -\lem{Lemma 2.1.}We discuss first the choice for $I_{k-1}^k$ -which is a generalization. We assume that $G^{k-1}$ is -obtained -from $G^k$ -by standard coarsening; that is, if $G^k$ is a tensor product -grid $G_{x}^k \times G_{y}^k \times G_{z}^k$, -$G^{k-1}=G_{x}^{k-1} \times G_{y}^{k-1} \times G_{z}^{k-1}$, -where $G_{x}^{k-1}$ is obtained by deleting every other grid -point of $G_x^k$ and similarly for $G_{y}^k$ and $G_{z}^k$. -\endlem - -% Use \fig to insert space for figures . - -\fig{10pc}{Fig. 1}{This is the caption for figure one.} - -To our knowledge, the m-tree previously has not been applied in this -fashion to the numerical factorization, but it has been used, -directly or indirectly, in several optimal order algorithms for -computing the fill-in during the symbolic factorization phase -[4] - [10], [5], [6]. In \S 1.3., we analyze the complexity of the old and new -approaches to the intersection problem for the special case of -an $n \times n$ grid ordered by nested dissection. The special -structure of this problem allows us to make exact estimates of -the complexity. To our knowledge, the m-tree previously has not been applied in this -fashion to the numerical factorization, but it has been used, -directly or indirectly, in several optimal order algorithms for -computing the fill-in during the symbolic factorization phase -[4] - [10], [5], [6]. - -% Use \headtwo for second level headings. They will be numbered automatically. - -\headtwo{Robustness}In \S 1.2, we review the bordering algorithm, and introduce -the sorting and intersection problems that arise in the -sparse formulation of the algorithm. - -\headtwo{Versatility} In \S 1.3., we analyze the complexity of the old and new -approaches to the intersection problem for the special case of -an $n \times n$ grid ordered by nested dissection. The special -structure of this problem allows us to make exact estimates of -the complexity. To our knowledge, the m-tree previously has not been applied in this -fashion to the numerical factorization, but it has been used, -directly or indirectly, in several optimal order algorithms for -computing the fill-in during the symbolic factorization phase -[4] - [10], [5], [6]. - - -% Use \headthree for third level headings. - -\headthree{Complexity.}For the old approach, we show that the -complexity of the intersection problem is $O(n^{3})$, the same -as the complexity of the numerical computations. For the -new approach, the complexity of the second part is reduced to -$O(n^{2} (\log n)^{2})$. - -% The command \Refs sets the word Reference as a heading and allows the proper -% amount of space before the start of the references. Each reference must -% begin with \ref\\. The article or title of the reference should be in -% italic. Use the \it command within brackets. End each reference with -% \endref and allow two returns between references. Use the command -% \sameauthor (see reference 8) when the same author or group of authors -% is listed consecutively. - -\Refs - -\ref 1\\R.~E. Bank, {\it PLTMG users' guide, edition 5.0}, tech. report, - Department of Mathematics, University of California, San Diego, CA, 1988.\endref - -\ref 2\\R.~E. Bank, T.~F. Dupont, and H.~Yserentant, {\it The hierarchical basis - multigrid method}, Numer. Math., 52 (1988), pp.~427--458.\endref - -\ref 3\\R.~E. Bank and R.~K. Smith, {\it General sparse elimination requires no - permanent integer storage}, SIAM J. Sci. Stat. Comput., 8 (1987), - pp.~574--584.\endref - -\ref 4\\S.~C. Eisenstat, M.~C. Gursky, M.~Schultz, and A.~Sherman, {\it - Algorithms and data structures for sparse symmetric gaussian elimination}, - SIAM J. Sci. Stat. Comput., 2 (1982), pp.~225--237.\endref - -\ref 5\\A.~George and J.~Liu, {\it Computer Solution of Large Sparse Positive - Definite Systems}, Prentice Hall, Englewood Cliffs, NJ, 1981.\endref - -\ref 6\\K.~H. Law and S.~J. Fenves, {\it A node addition model for symbolic - factorization}, ACM TOMS, 12 (1986), pp.~37--50.\endref - -\ref 7\\J.~W.~H. Liu, {\it A compact row storage scheme for cholesky factors - using elimination trees}, ACM TOMS, 12 (1986), pp.~127--148.\endref - -\ref 8\\\sameauthor , {\it The role of - elimination trees in sparse factorization}, Tech. Report CS-87-12,Department - of Computer Science, York University, Ontario, Canada, 1987.\endref - -\ref 9\\D.~J. Rose, {\it A graph theoretic study of the numeric solution of - sparse positive definite systems}, in Graph Theory and Computing, - Academic Press, New York, 1972.\endref - -\ref 10\\D.~J. Rose, R.~E. Tarjan, and G.~S. Lueker, {\it Algorithmic aspects of - vertex elimination on graphs}, SIAM J. Comput., 5 (1976), pp.~226--283.\endref - -\vfill\eject - -Extra page. -\vfill -\bye -%%% End of example file - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%CUT HERE%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -% This file may be freely distributed but may not be altered in any way. -% Any comments or questions regarding these macros should be directed to: - -% Corey Gray -% SIAM -% 3600 University City Science Center -% Philadelphia, PA 19104-2688 -% USA -% Telephone: (215) 382-9800 -% Fax: (215) 386-7999 -% e-mail: gray@siam.org - -% -% This is a file of macros and definitions for creating a chapter -% for publication in the NEC Proceedings Series using Plain TeX. - -% Report the version. -\message{*** NEC Plain TeX Proceedings Series macro package, version 1.0, -November 6, 1992.***} - -% Make the @ sign a letter for internal control sequences. -\catcode`\@=11 -% -% -% - - -\baselineskip=14truept - - -%%% DIMENSIONS %%% - -\hsize=30truepc -\vsize=49truepc -%\hoffset=.5in -\parindent=18truept -\def\firstpar{\parindent=0pt\global\everypar{\parindent=18truept}} -\parskip=0pt - - -%%% FONTS %%% - -\font\tenrm=cmr10 -\font\tenbf=cmbx10 -\font\tenit=cmti10 -\font\tensmc=cmcsc10 -\def\tenpoint{% - \def\rm{\tenrm}\def\bf{\tenbf}% - \def\it{\tenit}\def\smc{\tensmc} - \textfont0=\tenrm \scriptfont0=\sevenrm - \textfont1=\teni \scriptfont1=\seveni - \textfont2=\tensy \scriptfont2=\sevensy - \textfont3=\tenex \scriptfont3=\tenex -\baselineskip=12pt\rm}% - -\font\ninerm=cmr9 -\font\ninebf=cmbx9 -\font\nineit=cmti9 -\def\ninepoint{% - \def\rm{\ninerm}\def\bf{\ninebf}% - \def\it{\nineit}\baselineskip=11pt\rm}% - -\font\eightrm=cmr8 -\font\eightbf=cmbx8 -\font\eightit=cmti8 -\font\eighti=cmmi8 -\font\eightsy=cmsy8 -\def\eightpoint{% - \def\rm{\eightrm}\def\bf{\eightbf}% - \def\it{\eightit}\def\smc{\eightrm}\baselineskip=10pt\rm% - \textfont0=\eightrm \scriptfont0=\sixrm - \textfont1=\eighti \scriptfont1=\sixi - \textfont2=\eightsy \scriptfont2=\sixsy - \textfont3=\tenex \scriptfont3=\tenex -} - -\font\sixrm=cmr6 -\font\sixbf=cmbx6 -\font\sixi=cmmi6 -\font\sixsmc=cmr5 -\font\sixsy=cmsy6 -\def\sixpoint{% - \def\rm{\sixrm}\def\bf{\sixbf}% - \def\smc{\sixsmc}\baselineskip=8pt\rm}% - -\fontdimen13\tensy=2.6pt -\fontdimen14\tensy=2.6pt -\fontdimen15\tensy=2.6pt -\fontdimen16\tensy=1.2pt -\fontdimen17\tensy=1.2pt -\fontdimen18\tensy=1.2pt - -\font\eightrm=cmr8 -\font\ninerm=cmr9 -\font\elevenrm=cmr10 scaled\magstephalf -\font\fourteenrm=cmr10 scaled\magstep 1 -\font\eighteenrm=cmr10 scaled\magstep 3 -\font\twelvebf=cmbx10 scaled\magstep 1 -\font\elevenbf=cmbx10 scaled\magstephalf -\font\elevenit=cmti10 scaled\magstephalf -\font\elevensc=cmcsc10 scaled\magstephalf - -\def\theoremfont{\elevensc} -\def\textfont{\elevenrm} -\def\itfont{\elevenit} -\def\headfont{\twelvebf} -\def\smallheadfont{\elevenbf} -\def\titlefont{\eighteenrm} -\def\chapterfont{\fourteenrm} -\def\authorfont{\fourteenrm} -\def\rheadfont{\tenrm} -\def\abstractfont{\tenrm} -\def\smc{\tensmc} -\font\eightsmc=cmcsc8 - -\def\footnote#1{\baselineskip=11truept\edef\@sf{\spacefactor\the\spacefactor}#1\@sf - \insert\footins\bgroup\ninepoint\hsize=36pc - \interlinepenalty10000 \let\par=\endgraf - \leftskip=0pt \rightskip=0pt - \splittopskip=10pt plus 1pt minus 1pt \floatingpenalty=20000 -\smallskip -\item{#1}\bgroup\baselineskip=10pt\strut -\aftergroup\@foot\let\next} -\skip\footins=12pt plus 2pt minus 4pt -\dimen\footins=36pc - - - -%%% CHAPTER OPENING MACROS %%% - -\def\startchapter{\topinsert\vglue54pt\endinsert} - -\def\title#1\endtitle{\titlefont\centerline{#1}\vglue5pt}%\vskip40truept\tenrm} -\def\lasttitle#1\endlasttitle{\titlefont\centerline{#1}\vskip1.32truepc} -\def\author#1\endauthor{\authorfont\centerline{#1}\vglue8pt\textfont} -\def\lastauthor#1\endlastauthor{\authorfont\centerline{#1}\vglue2.56pc\textfont} -\def\abstract#1\endabstract{\baselineskip=12pt\leftskip=2.25pc - \rightskip=2.25pc\abstractfont{#1}\textfont} - -%%% COUNTERS FOR HEADINGS %%% - -\newcount\headcount -\headcount=1 -\newcount\seccount -\seccount=1 -\newcount\subseccount -\subseccount=1 -\def\secreset{\global\seccount=1} - \def\subsecreset{\global\subseccount=1} - -%%% HEADINGS %%% - -\def\headone#1{\baselineskip=14pt\leftskip=0pt\rightskip=0pt\vskip17truept\parindent=0pt -{\headfont\the\headcount\hskip14truept #1} -\par\nobreak\firstpar\global\advance\headcount by 0 - \global\advance\headcount by 1\secreset\vskip2truept\textfont} - -\def\headtwo#1{\advance\headcount by -1% - \vskip17truept\parindent=0pt{\headfont\the\headcount.% - \the\seccount\hskip14truept #1}%\enspace\ignorespaces\firstpar - \global\advance\headcount by 1\global\advance\seccount by 1 - \global\advance\subseccount by 1\subsecreset\vskip2pt\textfont} - - \def\headthree#1{\advance\headcount by -1\advance\seccount by -1 -% \advance\subseccount by -1% - \vskip17truept\parindent=0pt{\smallheadfont\the\headcount.% - \the\seccount.\the\subseccount\hskip11truept #1}\hskip6pt\ignorespaces - \firstpar\global\advance\headcount by 1\global\advance\seccount by 1 - \global\advance\subseccount by 1\textfont} - -%%% THEOREMS, PROOFS, DEFINITIONS, etc. %%% - -\def\thm#1{{\theoremfont -#1\enspace} -\hskip-5pt\begingroup\itfont\ignorespaces} - -\let\lem=\thm -\let\cor=\thm -\let\prop=\thm - -\def\endthm{\endgroup\textfont} -\let\endlem=\endthm -\let\endcor=\endthm -\let\endprop=\endthm - -\def\prf#1{{\itfont #1.}\textfont\enspace\ignorespaces} -\let\rem=\prf -\let\case=\prf - -\def\endprf{\textfont} -\let\endrem=\endprf -\let\endcase=\endprf - -\def\qed{{\qquad \vbox{\hrule\hbox{% - \vrule height1.3ex\hskip0.8ex\vrule}\hrule - }}\par} - -\def\dfn#1{{\theoremfont -#1\enspace} -\textfont\ignorespaces} - -\let\fact=\dfn - -\def\enddfn{\textfont} - -\let\endfact=\enddfn - -%%% FIGURES AND CAPTIONS %%% - - -\newcount\figcount -\figcount=1 - - -%\newcount\tablenumber -%\tablenumber=1 - -\def\\{\hfill\break} - -\newbox\TestBox -\newdimen\setwd -\newskip\belowcaptionskip -\belowcaptionskip=6pt plus 1pt - -\def\endinsert{\egroup % finish the \vbox - \if@mid \dimen@\ht\z@ \advance\dimen@\dp\z@ - \advance\dimen@12\p@ \advance\dimen@\pagetotal - \ifdim\dimen@>\pagegoal\@midfalse\p@gefalse\fi\fi - \if@mid\vskip\belowcaptionskip\box\z@\par \penalty-200\vskip\belowcaptionskip - \else\insert\topins{\penalty100 % floating insertion - \splittopskip\z@skip - \splitmaxdepth\maxdimen \floatingpenalty\z@ - \ifp@ge \dimen@\dp\z@ - \vbox to\vsize{\unvbox\z@\kern-\dimen@}% depth is zero - \else \box\z@\nobreak\vskip\belowcaptionskip\fi}\fi\endgroup} - - - - -\def\fig#1#2#3{% - \setbox\TestBox=\hbox{\tenpoint #3.}\setwd=\wd\TestBox - \topinsert - \vskip #1 - \vskip 12pt - \ifdim\setwd > 23pc - {\tenit{\smc #2.}\ \ #3} - \else - \centerline{\tenit\noindent - {\smc #2.}\ \ #3}\fi% - % \global\advance\figcount by 1 - \endinsert} - - - -%%% REFERENCES %%% - -\newdimen\refindent@ -\newdimen\refhangindent@ -\newbox\refbox@ -\setbox\refbox@=\hbox{\tenrm\baselineskip=11pt [00]}% Default 2 digits -\refindent@=\wd\refbox@ - -\def\resetrefindent#1{% - \setbox\refbox@=\hbox{\tenrm\baselineskip=11pt [#1]}% - \refindent@=\wd\refbox@} - -\def\Refs{% - \unskip\vskip1pc - \leftline{\noindent\headfont References}% - \penalty10000 - \vskip4pt - \penalty10000 - \refhangindent@=\refindent@ - \global\advance\refhangindent@ by .5em - \global\everypar{\hangindent\refhangindent@}% - \parindent=0pt\baselineskip=12pt\tenrm} - -\def\sameauthor{\leavevmode\vbox to 1ex{\vskip 0pt plus 100pt - \hbox to 2em{\leaders\hrule\hfil}\vskip 0pt plus 300pt}} - -\def\ref#1\\#2\endref{\leavevmode\hbox to \refindent@{\hfil[#1]}\enspace #2\par} - - -%%% OUTPUT %%% - -\def\rightheadline{\hfill\tenrm\rightrh\hskip2pc\tenrm\folio} -\def\leftheadline{\tenrm\folio\hskip2pc\tenrm\leftrh\hfill} - -\global\footline={\hss\tenrm\folio\hss}% first page - -\output{\plainoutput} -\def\plainoutput{\shipout\vbox{\makeheadline\pagebody\makefootline}% - \advancepageno - \ifnum\pageno>1 - \global\footline={\hfill}% - \fi - \ifodd\pageno - \global\headline={\rightheadline}% - \else - \global\headline={\leftheadline}% - \fi - \ifnum\outputpenalty>-\@MM \else\dosupereject\fi} -\def\pagebody{\vbox to\vsize{\boxmaxdepth\maxdepth \pagecontents}} -\def\makeheadline{\vbox to\z@{\vskip-22.5\p@ - \line{\vbox to8.5\p@{}\rheadfont\the\headline}\vss}% - \nointerlineskip} -\def\makefootline{\baselineskip24\p@\vskip-6\p@\line{\the\footline}} -\def\dosupereject{\ifnum\insertpenalties>\z@ % something is being held over - \line{}\kern-\topskip\nobreak\vfill\supereject\fi} - -\def\footnoterule{\vskip11pt\kern -4\p@\hrule width 3pc \kern 3.6\p@ } % rule = .4 pt high - -% Turn off @ as being a letter. -% -\catcode`\@=13 - -%end of style file - diff --git a/Master/texmf-dist/source/latex/siam/ptexpprt.all b/Master/texmf-dist/source/latex/siam/ptexpprt.all deleted file mode 100644 index fb644d0fdf3..00000000000 --- a/Master/texmf-dist/source/latex/siam/ptexpprt.all +++ /dev/null @@ -1,724 +0,0 @@ -%% This is ptexpprt.all. This file is to be used for creating a paper -%% in the ACM/SIAM Preprint series with Plain TeX. It consists of the following -%% two files: -%% -%% ptexpprt.tex ---- an example and documentation file -%% ptexpprt.sty ---- the macro file -%% -%% To use, cut this file apart at the appropriate places. You can run the -%% example file with the macros to get sample output. -%% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%% CUT HERE %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% -% -%%%%%%%%%%%%%%%%%%%%%%%%%% ptexpprt.tex %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% -% This is ptexpprt.tex, an example file for use with the ACM/SIAM Plain TeX -% Preprint Series macros. It is designed to produce double-column output. -% Comments are placed at the beginning and throughout this file. Please -% take the time to read them as they document how to use these macros. -% This file can be composed and printed out for use as sample output. - -% Any comments or questions regarding these macros should be directed to: -% -% Corey Gray -% SIAM -% 3600 University City Science Center -% Philadelphia, PA 19104-2688 -% USA -% Telephone: (215) 382-9800 -% Fax: (215) 386-7999 -% e-mail: siampubs@wharton.upenn.edu - - -% This file is to be used as an example for style only. It should not be read -% for content. - -%%%%%%%%%%%%%%% PLEASE NOTE THE FOLLOWING STYLE RESTRICTIONS %%%%%%%%%%%%%%% - -%% 1. You must use the numbered reference style([1],[2]), listing the -%% references at the end of the chapter either by order of citation -%% or alphabetically. -%% -%% 2. Unless otherwise stated by your editor, do your chapter as if it -%% is Chapter 1. -%% If you know which number your chapter is, you must do the following: -%% -%% Go into the style file (ptexfrnt.sty) and search for the -%% \def\chapter#1 definition. At the end of this definition -%% there is a command \headcount=1. Change the 1 to -%% the appropriate number. This change will cause the headings -%% in your chapter to match the chapter number. -%% -%% 3. This macro is set up for two levels of headings. The macro will -%% automatically number the headings for you. -%% -%% 4. The running heads are defined in the output routine. It will be -%% necessary for you to alter the information currently included. -%% To do this, go into the style file and search for OUTPUT. Once there, -%% scroll through the file until you see the command \def\rhead. Replace -%% CHAPTER TITLE with the title (or shortened title) of your paper. -%% Replace AUTHORS NAMES with the appropriate names. -%% Neither running head may be longer than 50 characters. -%% -%% 5. Theorems, Lemmas, Definitions, etc. are to be triple numbered, -%% indicating the chapter, section, and the occurence of that element -%% within that section. (For example, the first theorem in the second -%% section of chapter three would be numbered 3.2.1. This numbering must -%% be done manually. -%% -%% 6. Figures and equations must be manually double-numbered, indicating -%% chapter and occurence. Use \leqno for equation numbering. See the -%% example of \caption for figure numbering. -%% Note. Although not shown, tables must also be double-numbered. The -%% command \caption can also be used for table captions. -%% -%% 7. At the first occurence of each new element there is a description -%% of how to use the coding. -%% -%%%%%%% PLEASE NOTE THE FOLLOWING POTENTIAL PROBLEMS: -% -%% 1. A bug exists that prevents a page number from printing on the first -%% page of the paper. Please ignore this problem. It will be handled -%% after you submit your paper. -%% -%% 2. The use of \topinsert and \midinsert to allow space for figures can -%% result in unusual page breaks, or unusual looking pages in general. -%% If you encounter such a situation, contact the SIAM office at the -%% address listed above for instructions. -%% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -\input ptexpprt.sty -\voffset=.25in -\titlepage - -% It will be necessary to hard code the chapter title and chapter authors. -% You must decide where to break the lines. For the authors, please follow -% the following conventions: -% 1. If 2 authors are on a line, use \hskip4pc between them. If 3 authors, -% use \hskip2pc. Do not put more than 3 authors on the same line. -% 2. Use the following notation: asterisk, dagger, double-dagger, section -% symbol, paragraph symbol, double asterisk. If more are needed, contact -% the SIAM office. - -\centerline{\chapterfont Chapter 1} -\vskip2pt -\centerline{\titlefont SIAM/ACM Preprint Series Macros for -Plain TeX\footnote*{Supported by GSF grants ABC123, DEF456, and GHI 789.}} -\vskip15pt -\centerline{\authorfont J. Corey Gray\footnote\dag{Society for Industrial and -Applied Mathematics.}\hskip2pc Tricia Manning\footnote\ddag{Society for -Industrial and Applied Mathematics.}\hskip2pc Vickie Kearn\footnote\S{Society -for Industrial and Applied Mathematics.}} -\vskip2pc - -\begindoublecolumns - -% Use \headone for the first level headings. The macro will automatically -% number the headings. - -\headone{Problem Specification} -In this paper, we consider the solution of the $N \times N$ linear -system -$$A x = b\leqno(1.1)$$ -where $A$ is large, sparse, symmetric, and positive definite. We consider -the direct solution of by means of general sparse Gaussian -elimination. In such a procedure, we find a permutation matrix $P$, and -compute the decomposition -$$ -P A P^{t} = L D L^{t} -$$ -where $L$ is unit lower triangular and $D$ is diagonal. - -\headone{Design Considerations} -Several good ordering algorithms (nested dissection and minimum degree) -are available for computing $P$ [1], [2]. -Since our interest here does not -focus directly on the ordering, we assume for convenience that $P=I$, -or that $A$ has been preordered to reflect an appropriate choice of $P$. - -% Use \headtwo for second level headings. They will be numbered automatically. - -\headtwo{Robustness}In \S 1.2, we review the bordering algorithm, and introduce -the sorting and intersection problems that arise in the -sparse formulation of the algorithm. - -\headtwo{Versatility} In \S 1.3., we analyze the complexity of the old and new -approaches to the intersection problem for the special case of -an $n \times n$ grid ordered by nested dissection. The special -structure of this problem allows us to make exact estimates of -the complexity. To our knowledge, the m-tree previously has not been applied in -this -fashion to the numerical factorization, but it has been used, -directly or indirectly, in several optimal order algorithms for -computing the fill-in during the symbolic factorization phase -[4] - [10], [5], [6]. -This is accomplished by exploiting the m-tree, -a particular spanning tree for the graph of the filled-in matrix. -Our purpose here is to examine the nonnumerical complexity of the -sparse elimination algorithm given in [3]. -As was shown there, a general sparse elimination scheme based on the -bordering algorithm requires less storage for pointers and -row/column indices than more traditional implementations of general -sparse elimination. This is accomplished by exploiting the m-tree, -a particular spanning tree for the graph of the filled-in matrix. - - -% Use \thm and \endthm for theorems. They must be numbered manually. -% Lemmas (\lem \endlem), corollaries (\cor \endcor), and -% propositions (\prop \endprop) are coded the same as theorems and must -% also be numbered manually. - -\thm{Theorem 2.1.} The method was extended to three -dimensions. For the standard multigrid -coarsening -(in which, for a given grid, the next coarser grid has $1/8$ -as many points), anisotropic problems require plane -relaxation to -obtain a good smoothing factor.\endthm - -Several good ordering algorithms (nested dissection and minimum degree) -are available for computing $P$ [1], [2]. -Since our interest here does not -focus directly on the ordering, we assume for convenience that $P=I$, -or that $A$ has been preordered to reflect an appropriate choice of $P$. -Several good ordering algorithms (nested dissection and minimum degree) -are available for computing $P$ [1], [2]. -Since our interest here does not -focus directly on the ordering, we assume for convenience that $P=I$, -or that $A$ has been preordered to reflect an appropriate choice of $P$. - -% Use \prf to begin a proof. - -\prf{Proof} In this paper we consider two methods. The first method -is -basically the method considered with two differences: -first, we perform plane relaxation by a two-dimensional -multigrid method, and second, we use a slightly different -choice of -interpolation operator, which improves performance -for nearly singular problems. In the second method coarsening -is done by successively coarsening each. - -% Use \dfn to begin definitions. - -\dfn{Definition 1.2.1.}We describe the two methods in \S\ 1.2. This is a -definition in the plain tex macro. - -This is accomplished by exploiting the m-tree, -a particular spanning tree for the graph of the filled-in matrix. -Our purpose here is to examine the nonnumerical complexity of the -sparse elimination algorithm given in [3]. -As was shown there, a general sparse elimination scheme based on the -bordering algorithm requires less storage for pointers and -row/column indices than more traditional implementations of general -sparse elimination. This is accomplished by exploiting the m-tree, -a particular spanning tree for the graph of the filled-in matrix. -Our purpose here is to examine the nonnumerical complexity of the -sparse elimination algorithm given in [3]. -As was shown there, a general sparse elimination scheme based on the -bordering algorithm requires less storage for pointers and -row/column indices than more traditional implementations of general -sparse elimination. This is accomplished by exploiting the m-tree, -a particular spanning tree for the graph of the filled-in matrix. -Since our interest here does not -focus directly on the ordering, we assume for convenience that $P=I$, -or that $A$ has been preordered to reflect an appropriate choice of $P$. - - -To our knowledge, the m-tree previously has not been applied in this -fashion to the numerical factorization, but it has been used, -directly or indirectly, in several optimal order algorithms for -computing the fill-in during the symbolic factorization phase -[4] - [10], [5], [6]. In \S 1.3., we analyze the complexity of the old and new -approaches to the intersection problem for the special case of -an $n \times n$ grid ordered by nested dissection. The special -structure of this problem allows us to make exact estimates of -the complexity. To our knowledge, the m-tree previously has not been applied in -this -fashion to the numerical factorization, but it has been used, -directly or indirectly, in several optimal order algorithms for -computing the fill-in during the symbolic factorization phase -[4] - [10], [5], [6]. -Several good ordering algorithms (nested dissection and minimum degree) -are available for computing $P$ [1], [2]. -Since our interest here does not -focus directly on the ordering, we assume for convenience that $P=I$, -or that $A$ has been preordered to reflect an appropriate choice of $P$. -For the old approach, we show that the -complexity of the intersection problem is $O(n^{3})$, the same -as the complexity of the numerical computations. For the -new approach, the complexity of the second part is reduced to -$O(n^{2} (\log n)^{2})$. - -% Use \midinsert along with \caption to allow space for -% figures. See note above in problem section. -%\midinsert\vskip15.5pc\caption{Fig. 1.1. {\nineit This is figure 1.}} -% \endcaption\endinsert - -In this paper, we consider the solution of the $N \times N$ linear -system -where $A$ is large, sparse, symmetric, and positive definite. We consider -the direct solution of by means of general sparse Gaussian -elimination. In such a procedure, we find a permutation matrix $P$, and -compute the decomposition -where $L$ is unit lower triangular and $D$ is diagonal. - -\headone{Design Considerations} -Several good ordering algorithms (nested dissection and minimum degree) -are available for computing $P$ [1], [2]. -Since our interest here does not -focus directly on the ordering, we assume for convenience that $P=I$, -or that $A$ has been preordered to reflect an appropriate choice of $P$. - -Several good ordering algorithms (nested dissection and minimum degree) -are available for computing $P$ [1], [2]. -Since our interest here does not -focus directly on the ordering, we assume for convenience that $P=I$, -or that $A$ has been preordered to reflect an appropriate choice of $P$. -Several good ordering algorithms (nested dissection and minimum degree) -are available for computing $P$ [1], [2]. -Since our interest here does not -focus directly on the ordering, we assume for convenience that $P=I$, -or that $A$ has been preordered to reflect an appropriate choice of $P$. -Our purpose here is to examine the nonnumerical complexity of the -sparse elimination algorithm given in [3]. -As was shown there, a general sparse elimination scheme based on the -bordering algorithm requires less storage for pointers and -row/column indices than more traditional implementations of general -sparse elimination. This is accomplished by exploiting the m-tree, -a particular spanning tree for the graph of the filled-in matrix. -Since our interest here does not -focus directly on the ordering, we assume for convenience that $P=I$, -or that $A$ has been preordered to reflect an appropriate choice of $P$. - -% Use \lem and \endlem to begin and end lemmas. - -\lem{Lemma 2.1.}We discuss first the choice for $I_{k-1}^k$ -which is a generalization. We assume that $G^{k-1}$ is -obtained -from $G^k$ -by standard coarsening; that is, if $G^k$ is a tensor product -grid $G_{x}^k \times G_{y}^k \times G_{z}^k$, -$G^{k-1}=G_{x}^{k-1} \times G_{y}^{k-1} \times G_{z}^{k-1}$, -where $G_{x}^{k-1}$ is obtained by deleting every other grid -point of $G_x^k$ and similarly for $G_{y}^k$ and $G_{z}^k$. -\endlem - -To our knowledge, the m-tree previously has not been applied in this -fashion to the numerical factorization, but it has been used, -directly or indirectly, in several optimal order algorithms for -computing the fill-in during the symbolic factorization phase -[4] - [10], [5], [6]. In \S 1.3., we analyze the complexity of the old and new -approaches to the intersection problem for the special case of -an $n \times n$ grid ordered by nested dissection. The special -structure of this problem allows us to make exact estimates of -the complexity. To our knowledge, the m-tree previously has not been applied in -this -fashion to the numerical factorization, but it has been used, -directly or indirectly, in several optimal order algorithms for -computing the fill-in during the symbolic factorization phase -[4] - [10], [5], [6]. - -% Use \headtwo for second level headings. They will be numbered automatically. - -\headone{Problem Solving}In \S 1.2, we review the bordering algorithm, and -introduce -the sorting and intersection problems that arise in the -sparse formulation of the algorithm. - -\headtwo{Versatility} In \S 1.3., we analyze the complexity of the old and new -approaches to the intersection problem for the special case of -an $n \times n$ grid ordered by nested dissection. The special -structure of this problem allows us to make exact estimates of -the complexity. To our knowledge, the m-tree previously has not been applied in -this -fashion to the numerical factorization, but it has been used, -directly or indirectly, in several optimal order algorithms for -computing the fill-in during the symbolic factorization phase -[4] - [10], [5], [6]. - - -\headtwo{Complexity}For the old approach, we show that the -complexity of the intersection problem is $O(n^{3})$, the same -as the complexity of the numerical computations. For the -new approach, the complexity of the second part is reduced to -$O(n^{2} (\log n)^{2})$. - -To our knowledge, the m-tree previously has not been applied in this -fashion to the numerical factorization, but it has been used, -directly or indirectly, in several optimal order algorithms for -computing the fill-in during the symbolic factorization phase -[4] - [10], [5], [6]. In \S 1.3., we analyze the complexity of the old and new -approaches to the intersection problem for the special case of -an $n \times n$ grid ordered by nested dissection. The special -structure of this problem allows us to make exact estimates of -the complexity. To our knowledge, the m-tree previously has not been applied in -this -fashion to the numerical factorization, but it has been used, -directly or indirectly, in several optimal order algorithms for -computing the fill-in during the symbolic factorization phase -[4] - [10], [5], [6]. - -% The command \Refs sets the word Reference as a heading and allows the proper -% amount of space before the start of the references. Each reference must -% begin with \ref\\. The article or title of the reference should be in -% italic. Use the \it command within brackets. End each reference with -% \endref and allow two returns between references. Use the command -% \sameauthor (see reference 8) when the same author or group of authors -% is listed consecutively. - -\Refs - -\ref 1\\R.~E. Bank, {\it PLTMG users' guide, edition 5.0}, tech. report, - Department of Mathematics, University of California, San Diego, CA, -1988.\endref - -\ref 2\\R.~E. Bank, T.~F. Dupont, and H.~Yserentant, {\it The hierarchical basis - multigrid method}, Numer. Math., 52 (1988), pp.~427--458.\endref - -\ref 3\\R.~E. Bank and R.~K. Smith, {\it General sparse elimination requires no - permanent integer storage}, SIAM J. Sci. Stat. Comput., 8 (1987), - pp.~574--584.\endref - -\ref 4\\S.~C. Eisenstat, M.~C. Gursky, M.~Schultz, and A.~Sherman, {\it - Algorithms and data structures for sparse symmetric gaussian elimination}, - SIAM J. Sci. Stat. Comput., 2 (1982), pp.~225--237.\endref - -\ref 5\\A.~George and J.~Liu, {\it Computer Solution of Large Positive - Definite Systems}, Prentice Hall, Englewood Cliffs, NJ, 1981.\endref - -\ref 6\\K.~H. Law and S.~J. Fenves, {\it A node addition model for symbolic - factorization}, ACM TOMS, 12 (1986), pp.~37--50.\endref - -\ref 7\\J.~W.~H. Liu, {\it A compact row storage scheme for factors - using elimination trees}, ACM TOMS, 12 (1986), pp.~127--148.\endref - -\ref 8\\\sameauthor , {\it The role of - elimination trees in sparse factorization}, Tech. Report CS-87-12,Department - of Computer Science, York University, Ontario, Canada, 1987.\endref - -\ref 9\\D.~J. Rose, {\it A graph theoretic study of the numeric solution of - sparse positive definite systems}, in Graph Theory and Computing, - Academic Press, New York, 1972.\endref - -\ref 10\\D.~J. Rose, R.~E. Tarjan, and G.~S. Lueker, {\it Algorithmic aspects of - vertex elimination on graphs}, SIAM J. Comput., 5 (1976), pp.~226--283.\endref -\enddoublecolumns - -\bye -%% -%% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%% CUT HERE %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% -% -%%%%%%%%%%%%%%%%%%%%%%%%%% ptexpprt.sty %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% -% This is a file of macros and definitions for creating a chapter -% for publication in the ACM/SIAM Preprint Series using Plain TeX. -% This file may be freely distributed but may not be altered in any way. -% Any comments or questions regarding these macros should be directed to: - -% Corey Gray -% SIAM -% 3600 University City Science Center -% Philadelphia, PA 19104-2688 -% USA -% Telephone: (215) 382-9800 -% Fax: (215) 386-7999 -% e-mail: siampubs@wharton.upenn.edu - -% - -% Report the version. -\message{*** ACM/SIAM Plain TeX Preprint Series macro package, version 1.0, -September 24, 1990.***} - -% Make the @ sign a letter for internal control sequences. -\catcode`\@=11 -% -% -% - - - -%%% DIMENSIONS %%% - -\newdimen\pagewidth -\hsize=41pc -\pagewidth=\hsize -\newdimen\pageheight -\vsize=50pc -\pageheight=\vsize -\newdimen\ruleht -\ruleht=.5pt -\maxdepth=2.2pt - -\parindent=18truept -\def\firstpar{\parindent=0pt\global\everypar{\parindent=18truept}} -\parskip=0pt plus 1pt - - -%%% FONTS %%% - -\font\tenrm=cmr10 -\font\tenbf=cmbx10 -\font\tenit=cmti10 -\font\tensmc=cmcsc10 -\def\tenpoint{% - \def\rm{\tenrm}\def\bf{\tenbf}% - \def\it{\tenit}\def\smc{\tensmc} - \textfont0=\tenrm \scriptfont0=\sevenrm - \textfont1=\teni \scriptfont1=\seveni - \textfont2=\tensy \scriptfont2=\sevensy - \textfont3=\tenex \scriptfont3=\tenex -\baselineskip=12pt\rm}% - -\font\ninerm=cmr9 -\font\ninebf=cmbx9 -\font\nineit=cmti9 -\def\ninepoint{% - \def\rm{\ninerm}\def\bf{\ninebf}% - \def\it{\nineit}\baselineskip=11pt\rm}% - -\font\eightrm=cmr8 -\font\eightbf=cmbx8 -\font\eightit=cmti8 -\font\eighti=cmmi8 -\font\eightsy=cmsy8 -\def\eightpoint{% - \def\rm{\eightrm}\def\bf{\eightbf}% - \def\it{\eightit}\def\smc{\eightrm}\baselineskip=10pt\rm% - \textfont0=\eightrm \scriptfont0=\sixrm - \textfont1=\eighti \scriptfont1=\sixi - \textfont2=\eightsy \scriptfont2=\sixsy - \textfont3=\tenex \scriptfont3=\tenex -} - -\font\sixrm=cmr6 -\font\sixbf=cmbx6 -\font\sixi=cmmi6 -\font\sixsmc=cmr5 -\font\sixsy=cmsy6 -\def\sixpoint{% - \def\rm{\sixrm}\def\bf{\sixbf}% - \def\smc{\sixsmc}\baselineskip=8pt\rm}% - -\fontdimen13\tensy=2.6pt -\fontdimen14\tensy=2.6pt -\fontdimen15\tensy=2.6pt -\fontdimen16\tensy=1.2pt -\fontdimen17\tensy=1.2pt -\fontdimen18\tensy=1.2pt - -\font\eightrm=cmr8 -\font\ninerm=cmr9 -\font\twelverm=cmr10 scaled\magstep1 -\font\twelvebf=cmbx10 scaled\magstep 1 -\font\sixteenrm=cmr10 scaled\magstep2 -\def\titlefont{\sixteenrm} -\def\chapterfont{\twelvebf} -\def\authorfont{\twelverm} -\def\rheadfont{\tenrm} -\def\smc{\tensmc} - - - - -%%% COUNTERS FOR HEADINGS %%% - -\newcount\headcount -\headcount=1 -\newcount\seccount -\seccount=1 -\newcount\subseccount -\subseccount=1 -\def\reset{\global\seccount=1} -\global\headcount=0 - -%%% HEADINGS %%% - -\def\headone#1{\global\advance\headcount by 1 -\vskip12truept\parindent=0pt{\tenpoint\bf\the\headcount -\hskip11truept #1.}\par\nobreak\firstpar\global\advance\headcount by 0 - %\global\advance\seccount by 1 -\reset\vskip2truept} - -\def\headtwo#1{%\advance\seccount by -1% - \vskip12truept\parindent=0pt{\tenpoint\bf\the\headcount.% - \the\seccount\hskip11truept #1.}\enspace\ignorespaces\firstpar - \global\advance\headcount by 0\global\advance\seccount by 1} -% \global\advance\subseccount by 1} - - -%%% THEOREMS, PROOFS, DEFINITIONS, etc. %%% - -\def\thm#1{{\smc -#1\enspace} -\begingroup\it\ignorespaces\firstpar} - -\let\lem=\thm -\let\cor=\thm -\let\prop=\thm - -\def\endthm{\endgroup} -\let\endlem=\endthm -\let\endcor=\endthm -\let\endprop=\endthm - -\def\prf#1{{\it #1.}\rm\enspace\ignorespaces} -\let\rem=\prf -\let\case=\prf - - -\def\dfn#1{{\smc -#1\enspace} -\rm\ignorespaces} - - - -%%% FIGURES AND CAPTIONS %%% - -\def\caption#1\endcaption{\vskip18pt\ninerm\centerline{#1}\vskip18pt\tenrm} - -\newinsert\topins \newif\ifp@ge \newif\if@mid -\def\topinsert{\@midfalse\p@gefalse\@ins} -\def\midinsert{\@midtrue\@ins} -\def\pageinsert{\@midfalse\p@getrue\@ins} -\skip\topins=0pt %no space added when a topinsert is present -\count\topins=1000 %magnification factor (1 to 1) -\dimen\topins=\maxdimen -\def\@ins{\par\begingroup\setbox0=\vbox\bgroup} -\def\endinsert{\egroup - \if@mid \dimen@=\ht0 \advance\dimen@ by\dp0 - \advance\dimen@ by12\p@ \advance\dimen@ by\pagetotal - \ifdim\dimen@>\pagegoal \@midfalse\p@gefalse\fi\fi - \if@mid \bigskip \box0 \bigbreak - \else\insert\topins{\penalty100 - \splittopskip=0pt \splitmaxdepth=\maxdimen \floatingpenalty=0 - \ifp@ge \dimen@=\dp0 - \vbox to\vsize{\unvbox0 \kern-\dimen@} - \else \box0 \nobreak\bigskip\fi}\fi\endgroup} - - -%%% REFERENCES %%% - -\newdimen\refindent@ -\newdimen\refhangindent@ -\newbox\refbox@ -\setbox\refbox@=\hbox{\ninepoint\rm\baselineskip=11pt [00]}% Default 2 digits -\refindent@=\wd\refbox@ - -\def\resetrefindent#1{% - \setbox\refbox@=\hbox{\ninepoint\rm\baselineskip=11pt [#1]}% - \refindent@=\wd\refbox@} - -\def\Refs{% - \unskip\vskip1pc - \leftline{\noindent\tenpoint\bf References}% - \penalty10000 - \vskip4pt - \penalty10000 - \refhangindent@=\refindent@ - \global\advance\refhangindent@ by .5em - \global\everypar{\hangindent\refhangindent@}% - \parindent=0pt\ninepoint\rm} - -\def\sameauthor{\leavevmode\vbox to 1ex{\vskip 0pt plus 100pt - \hbox to 2em{\leaders\hrule\hfil}\vskip 0pt plus 300pt}} - -\def\ref#1\\#2\endref{\leavevmode\hbox to \refindent@{\hfil[#1]}\enspace #2\par} - - -%%% OUTPUT %%% - -\newinsert\margin -\dimen\margin=\maxdimen -\count\margin=0 \skip\margin=0pt - - -\def\footnote#1{\edef\@sf{\spacefactor\the\spacefactor}#1\@sf - \insert\footins\bgroup\eightpoint\hsize=30pc - \interlinepenalty100 \let\par=\endgraf - \leftskip=0pt \rightskip=0pt - \splittopskip=10pt plus 1pt minus 1pt \floatingpenalty=20000 -\smallskip -\item{#1}\bgroup\strut\aftergroup\@foot\let\next} -\skip\footins=6pt plus 2pt minus 4pt -\dimen\footins=30pc - -\newif\iftitle - - -\def\titlepage{\global\titletrue\footline={\hss\ninepoint\rm\folio\hss}} -\def\rhead{\ifodd\pageno CHAPTER TITLE - \else AUTHORS NAMES\fi} - -\def\makefootline{\ifnum\pageno>1\global\footline={\hfill}\fi - \baselineskip24\p@\vskip12\p@\fullline{\the\footline}} -\def\leftheadline{\hbox to \pagewidth{ - \vbox to 10pt{} - {\kern-8pt\tenrm\folio\hfill\ninerm\rhead}}} -\def\rightheadline{\hbox to \pagewidth{ - \vbox to 10pt{} - \kern-8pt\ninerm\rhead\hfil - {\kern-1pc\tenrm\folio}}} - -\def\onepageout#1{\shipout\vbox{ -\offinterlineskip - \vbox to 2.25pc{% - \iftitle \global\titlefalse -% \setcornerrules - \else\ifodd\pageno\rightheadline\else\leftheadline\fi\fi \vfill} -\vbox to \pageheight{ - \ifvoid\margin\else - \rlap{\kern31pc\vbox to0pt{\kern4pt\box\margin \vss}}\fi - #1 % -\ifvoid\footins\else - \vskip\skip\footins \kern 0pt - \hrule height\ruleht width 2.5pc \kern-\ruleht \kern 0pt - \unvbox\footins\fi -\boxmaxdepth=\maxdepth}} -\advancepageno} - -\def\setcornerrules{\hbox to \pagewidth{ - \vrule width 1pc height\ruleht \hfil \vrule width 1pc} - \hbox to \pagewidth{\llap{\sevenrm(page \folio)\kern1pc} - \vrule height1pc width\ruleht depth0pt - \hfil \vrule width\ruleht depth0pt}} -\output{\onepageout{\unvbox255}} - -\newbox\partialpage -\def\begindoublecolumns{\begingroup - \output={\global\setbox\partialpage=\vbox{\unvbox255\bigskip}}\eject - \output={\doublecolumnout} \hsize=20pc \vsize=101pc} -\def\enddoublecolumns{\output={\balancecolumns}\eject - \endgroup \pagegoal=\vsize} - -\def\doublecolumnout{\splittopskip=\topskip \splitmaxdepth=\maxdepth - \dimen@=50pc \advance\dimen@ by-\ht\partialpage - \setbox0=\vsplit255 to\dimen@ \setbox2=\vsplit255 to\dimen@ - \onepageout\pagesofar \unvbox255 \penalty\outputpenalty} -\def\pagesofar{\unvbox\partialpage - \wd0=\hsize \wd2=\hsize \hbox to\pagewidth{\box0\hfil\box2}} -\def\balancecolumns{\setbox0=\vbox{\unvbox255} \dimen@=\ht0 - \advance\dimen@ by\topskip \advance\dimen@ by-\baselineskip - \divide\dimen@ by2 \splittopskip=\topskip -{\vbadness=10000 \loop \global\setbox3=\copy0 - \global\setbox1=\vsplit3 to\dimen@ - \ifdim\ht3>\dimen@ \global\advance\dimen@ by1pt \repeat} - \setbox0=\vbox to\dimen@{\unvbox1} \setbox2=\vbox to\dimen@{\unvbox 3} -\pagesofar} - - - - -% Turn off @ as being a letter. -% -\catcode`\@=13 - -% End of ptexpprt.sty - - -CUT HERE............ diff --git a/Master/texmf-dist/source/latex/siam/ptexproc.all b/Master/texmf-dist/source/latex/siam/ptexproc.all deleted file mode 100644 index 728b5da243d..00000000000 --- a/Master/texmf-dist/source/latex/siam/ptexproc.all +++ /dev/null @@ -1,704 +0,0 @@ - - -This file constitutes the full distribution of SIAM Proceedings Series -Plain TeX macros. The files are: - -ptexproc.tex (An example file, also containing documentation) - -ptexproc.sty (the style file) - -To use these macros, separate at the indicated cut lines. - -%%%%%%%%%%%%%%%%%%%%%%%%%CUT HERE%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -% This is ptexproc.tex, an example file for use with the SIAM Plain TeX -% Proceedings Series macros. Comments are placed at the beginning and -% throughout this file. Please take the time to read them as they document -% how to use these macros. This file can be composed and printed out for -% use as sample output. Please ignore the underfull \vbox on page 3. - -% Any comments or questions regarding these macros should be directed to: -% -% Corey Gray -% SIAM -% 3600 University City Science Center -% Philadelphia, PA 19104-2688 -% USA -% Telephone: (215) 382-9800 -% Fax: (215) 386-7999 -% e-mail: gray@siam.org - - -% This file is to be used as an example for style only. It should not be read -% for content. - -%%%%%%%%%%%%%%% PLEASE NOTE THE FOLLOWING STYLE RESTRICTIONS %%%%%%%%%%%%%%% - -%% 1. You must use the numbered reference style([1],[2]), listing the -%% references at the end of the chapter either by order of citation -%% or alphabetically. -%% -%% 2. This macro is set up for three levels of headings. Use the commands -%% \headone, \headtwo, and \headthree. The macro will automatically -%% number the headings. -%% -%% 3. The running heads are defined by the commands \def\leftrh{} and -%% \def\rightrh{}. You must fill in the empty field of these commands -%% with the appropriate information. The left running head should be the -%% authors names. For papers with multiple authors, please follow these -%% rules; for two authors type {Author 1 and Author 2}; for more than two -%% authors type {Author 1 et al.}. The right running head is the title of -%% the paper. If the title is more than 50 characters, including spaces, -%% please provide a shortened version. All information should be typed -%% initial cap and lower case. -%% -%% 5. Theorems, Lemmas, Definitions, etc. are to be double-numbered, -%% indicating the section and the occurrence of that element -%% within that section. (For example, the first theorem in the second -%% section would be numbered 2.1.) This numbering must -%% be done manually. -%% -%% 6. Proofs are handled by \prf\endprf. If you want to use an end-of-proof -%% box, insert \qed right before the \endprf command. -%% -%% 7. Figures and equations must be manually single-numbered. Use \leqno -%% for equation numbering. The macro provides the \fig for including -%% figures. This command consists of three fields. The first field is -%% used for inserting the appropriate space for the figure. The second -%% field is the figure number. The third field is the caption. See the -%% example included in this file. SIAM supports the use of psfig for -%% including Postscript figures. All Postscript figures should be sent -%% as separate files. A hardcopy version of all Postscript figures is -%% also required. See note regarding this under How to Submit Your Paper. -%% -%% 8. Use of \title\endtitle and \lasttitle\endlastitle. -%% This macro package provides two possible commands for handling the -%% title of your paper. The commands \title\endtitle should be used for -%% all lines except the last line of multiple line titles. The commands -%% \lasttitle\endlasttitle should be used for the last line of multiple -%% line titles. In the case of a single line title, \lasttitle\endlasttitle -%% should be used. -%% -%% 9. Use of \author\endauthor and \lastauthor\endlastauthor. -%% As in the title macro, two possible commands are provided for the -%% author. The commands \author\endauthor should be used for the first -%% line of authors if there are more than one line. The commands -%% \lastauthor\endlastauthor should be used for the last line -%% of multiple lines of authors. In the case of a single line of authors, -%% \lastauthor\endlastauthor should be used. A maximum of four authors -%% should be placed on any one line. The appropriate space must also be -%% hard coded between authors on the same line. The spacing is as follows: -%% -%% If 2 authors; \hskip4pc between -%% If 3 authors; \hskip3pc between -%% If 4 authors; \hskip2pc between -%% -%% 10. Grant information and author affiliations. -%% This information is included by using the \footnote command and the -%% appropriate footnote symbol. SIAM uses footnote symbols in a -%% particular order. Below is a list of these symbols: -%% -%% asterisk -%% single-dagger -%% double-dagger -%% section sign -%% paragraph -%% parallel -%% double asterisk -%% double single-dagger -%% double double-dagger -%% -%% For illustrative purposes, all footnote symbols have been used in the -%% example file. -%% -%% A note regarding \footnote. This command seems to leave extra white -%% space between footnotes. This is quite evident in the example file. If -%% any user of these macros has a solution to this problem, I would -%% appreciate hearing from you. Send your comments to: gray@siam.org. -%% -%% The following general rules apply for including grants and affiliations: -%% a) If there is a single grant for the paper, then the grant -%% information should be footnoted to the title. -%% b) If there is more than one grant, included the grant information -%% with each authors affiliation. -%% c) If there are different grants for the paper but the authors share -%% the same affiliation, footnote the grant information to the title. -%% For example, The work of the first author was supported by xyz. -%% The work of the second author was supported by abc. And so on. -%% -%% -%% 11. Special fonts. -%% SIAM supports the use of AMS-TeX fonts version 2.0 and later. As -%% described in the manual for these fonts, they can be included by -%% \input{amssym.def} and \input{amssym.tex}. -%% -%% 12. How to Submit Your Paper. -%% The electronic version of your paper should be sent to proceed@siam.org. -%% A hardcopy version should also be submitted. Instructions are included -%% in your acceptance letter. Please be sure to send hardcopy -%% versions of any Postscript figures you have submitted electronically. -%% Be sure to return your signed Copyright Transfer Agreement. We cannot -%% publish your paper without one.%% -%% -%% - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -\input ptexproc.sty - -\def\leftrh{Gray et al.} -\def\rightrh{SIAM Proceedings Series Macros} - -\startchapter %Place this command at the beginning of the file immediately - %after the \input command. - - - -\title Chapter 1\endtitle -\title SIAM Proceedings Series Macros\endtitle -\lasttitle for Use with Plain TeX\footnote*{Any information -regarding grants should be placed here.}\endlasttitle - -\author J. Corey Gray\footnote{$^{\dag}$}{Production Manager, Society for -Industrial and Applied Mathematics, Philadelphia, PA.} -\hskip2truepc Tricia Manning\footnote{$^{\ddag}$}{Publications -Specialist, Society for Industrial and Applied Mathematics, Philadelphia, -PA.} -\hskip2truepc Vickie Kearn\footnote{$^{\S}$}{Publisher, Society for Industrial -and Applied Mathematics, Philadelphia, PA.} -\hskip2truepc Nancy Abbott\footnote{$^{\P}$}{Design Supervisor, Society for -Industrial and Applied Mathematics, Philadelphia, PA.} -\endauthor -\lastauthor Sue Ciambrano\footnote{$^{\parallel}$}{Acquisition Editor, Society for -Industrial and Applied Mathematics, Philadelphia, PA.} -\hskip2truepc Paul Duggan\footnote{$^{**}$}{Composition -Specialist, Society for Industrial and Applied Mathematics, Philadelphia, -PA.} -\hskip2truepc Robbi Anne Albert\footnote{$^{\dagger\dagger}$}{Production, -Assistant, Society for Industrial -and Applied Mathematics, Philadelphia, PA.} -\hskip2truepc Jean Anderson\footnote{$^{\ddag\ddag}$}{Composition Coordinator, Society for -Industrial and Applied Mathematics, Philadelphia, PA.} -\endlastauthor - -% Use \headone for the first level headings. The macro will automatically -% number the headings. - -\centerline{\bf Abstract} -\abstract An equivalence is shown between realizability of input/output (i/o) operators by -rational control systems and high-order algebraic differential equations for -i/o pairs. This generalizes, to nonlinear systems, the equivalence -between autoregressive representations and finite dimensional linear -realizability.\endabstract - - -\headone{Problem Specification} -In this paper, we consider the solution of the $N \times N$ linear -system -$$A x = b\leqno (1)$$ -where $A$ is large, sparse, symmetric, and positive definite. We consider -the direct solution of by means of general sparse Gaussian -elimination. In such a procedure, we find a permutation matrix $P$, and -compute the decomposition -$$ -P A P^{t} = L D L^{t} -\leqno (2)$$ - -\noindent where $L$ is unit lower triangular and $D$ is diagonal. - - -\headone{Design Considerations} -Several good ordering algorithms (nested dissection and minimum degree) -are available for computing $P$ [1], [2]. -Since our interest here does not -focus directly on the ordering, we assume for convenience that $P=I$, -or that $A$ has been preordered to reflect an appropriate choice of $P$. - -% Use \thm and \endthm for theorems. They must be numbered manually. -% Lemmas (\lem \endlem), corollaries (\cor \endcor), and -% propositions (\prop \endprop) are coded the same as theorems and must -% also be numbered manually. - -\thm{Theorem 2.1.} The method was extended to three -dimensions. For the standard multigrid -coarsening -(in which, for a given grid, the next coarser grid has $1/8$ -as many points), anisotropic problems require plane -relaxation to -obtain a good smoothing factor.\endthm - -Several good ordering algorithms (nested dissection and minimum degree) -are available for computing $P$ [1], [2]. -Since our interest here does not -focus directly on the ordering, we assume for convenience that $P=I$, -or that $A$ has been preordered to reflect an appropriate choice of $P$. -Several good ordering algorithms (nested dissection and minimum degree) -are available for computing $P$ [1], [2]. -Since our interest here does not -focus directly on the ordering, we assume for convenience that $P=I$, -or that $A$ has been preordered to reflect an appropriate choice of $P$. - -% Use \prf and \endprf to begin and end a proof. -% The use of \qed will produce an end-of-proof box. - -\prf{Proof} In this paper we consider two methods. The first method -is -basically the method considered with two differences: -first, we perform plane relaxation by a two-dimensional -multigrid method, and second, we use a slightly different -choice of -interpolation operator, which improves performance -for nearly singular problems. In the second method coarsening -is done by successively coarsening each.\qed\endprf - -% Use \dfn and \enddfn to begin and end definitions. - -\dfn{Definition 2.1.}We describe the two methods in \S\ 1.2. This is a -definition in the plain tex macro.\enddfn - -This is accomplished by exploiting the m-tree, -a particular spanning tree for the graph of the filled-in matrix. -Our purpose here is to examine the nonnumerical complexity of the -sparse elimination algorithm given in [3]. -As was shown there, a general sparse elimination scheme based on the -bordering algorithm requires less storage for pointers and -row/column indices than more traditional implementations of general -sparse elimination. This is accomplished by exploiting the m-tree, -a particular spanning tree for the graph of the filled-in matrix. - - -Our purpose here is to examine the nonnumerical complexity of the -sparse elimination algorithm given in [3]. -As was shown there, a general sparse elimination scheme based on the -bordering algorithm requires less storage for pointers and -row/column indices than more traditional implementations of general -sparse elimination. This is accomplished by exploiting the m-tree, -a particular spanning tree for the graph of the filled-in matrix. -Since our interest here does not -focus directly on the ordering, we assume for convenience that $P=I$, -or that $A$ has been preordered to reflect an appropriate choice of $P$. - -% Use \lem and \endlem to begin and end lemmas. - -\lem{Lemma 2.1.}We discuss first the choice for $I_{k-1}^k$ -which is a generalization. We assume that $G^{k-1}$ is -obtained -from $G^k$ -by standard coarsening; that is, if $G^k$ is a tensor product -grid $G_{x}^k \times G_{y}^k \times G_{z}^k$, -$G^{k-1}=G_{x}^{k-1} \times G_{y}^{k-1} \times G_{z}^{k-1}$, -where $G_{x}^{k-1}$ is obtained by deleting every other grid -point of $G_x^k$ and similarly for $G_{y}^k$ and $G_{z}^k$. -\endlem - -% Use \fig to insert space for figures . - -\fig{10pc}{Fig. 1}{This is the caption for figure one.} - -To our knowledge, the m-tree previously has not been applied in this -fashion to the numerical factorization, but it has been used, -directly or indirectly, in several optimal order algorithms for -computing the fill-in during the symbolic factorization phase -[4] - [10], [5], [6]. In \S 1.3., we analyze the complexity of the old and new -approaches to the intersection problem for the special case of -an $n \times n$ grid ordered by nested dissection. The special -structure of this problem allows us to make exact estimates of -the complexity. To our knowledge, the m-tree previously has not been applied in this -fashion to the numerical factorization, but it has been used, -directly or indirectly, in several optimal order algorithms for -computing the fill-in during the symbolic factorization phase -[4] - [10], [5], [6]. - -% Use \headtwo for second level headings. They will be numbered automatically. - -\headtwo{Robustness}In \S 1.2, we review the bordering algorithm, and introduce -the sorting and intersection problems that arise in the -sparse formulation of the algorithm. - -\headtwo{Versatility} In \S 1.3., we analyze the complexity of the old and new -approaches to the intersection problem for the special case of -an $n \times n$ grid ordered by nested dissection. The special -structure of this problem allows us to make exact estimates of -the complexity. To our knowledge, the m-tree previously has not been applied in this -fashion to the numerical factorization, but it has been used, -directly or indirectly, in several optimal order algorithms for -computing the fill-in during the symbolic factorization phase -[4] - [10], [5], [6]. - - -% Use \headthree for third level headings. - -\headthree{Complexity.}For the old approach, we show that the -complexity of the intersection problem is $O(n^{3})$, the same -as the complexity of the numerical computations. For the -new approach, the complexity of the second part is reduced to -$O(n^{2} (\log n)^{2})$. - -% The command \Refs sets the word Reference as a heading and allows the proper -% amount of space before the start of the references. Each reference must -% begin with \ref\\. The article or title of the reference should be in -% italic. Use the \it command within brackets. End each reference with -% \endref and allow two returns between references. Use the command -% \sameauthor (see reference 8) when the same author or group of authors -% is listed consecutively. - -\Refs - -\ref 1\\R.~E. Bank, {\it PLTMG users' guide, edition 5.0}, tech. report, - Department of Mathematics, University of California, San Diego, CA, 1988.\endref - -\ref 2\\R.~E. Bank, T.~F. Dupont, and H.~Yserentant, {\it The hierarchical basis - multigrid method}, Numer. Math., 52 (1988), pp.~427--458.\endref - -\ref 3\\R.~E. Bank and R.~K. Smith, {\it General sparse elimination requires no - permanent integer storage}, SIAM J. Sci. Stat. Comput., 8 (1987), - pp.~574--584.\endref - -\ref 4\\S.~C. Eisenstat, M.~C. Gursky, M.~Schultz, and A.~Sherman, {\it - Algorithms and data structures for sparse symmetric gaussian elimination}, - SIAM J. Sci. Stat. Comput., 2 (1982), pp.~225--237.\endref - -\ref 5\\A.~George and J.~Liu, {\it Computer Solution of Large Sparse Positive - Definite Systems}, Prentice Hall, Englewood Cliffs, NJ, 1981.\endref - -\ref 6\\K.~H. Law and S.~J. Fenves, {\it A node addition model for symbolic - factorization}, ACM TOMS, 12 (1986), pp.~37--50.\endref - -\ref 7\\J.~W.~H. Liu, {\it A compact row storage scheme for cholesky factors - using elimination trees}, ACM TOMS, 12 (1986), pp.~127--148.\endref - -\ref 8\\\sameauthor , {\it The role of - elimination trees in sparse factorization}, Tech. Report CS-87-12,Department - of Computer Science, York University, Ontario, Canada, 1987.\endref - -\ref 9\\D.~J. Rose, {\it A graph theoretic study of the numeric solution of - sparse positive definite systems}, in Graph Theory and Computing, - Academic Press, New York, 1972.\endref - -\ref 10\\D.~J. Rose, R.~E. Tarjan, and G.~S. Lueker, {\it Algorithmic aspects of - vertex elimination on graphs}, SIAM J. Comput., 5 (1976), pp.~226--283.\endref - - -\bye - -%end of example file -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%CUT HERE%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -% This is ptexproc.sty -% This file may be freely distributed but may not be altered in any way. -% Any comments or questions regarding these macros should be directed to: - -% Corey Gray -% SIAM -% 3600 University City Science Center -% Philadelphia, PA 19104-2688 -% USA -% Telephone: (215) 382-9800 -% Fax: (215) 386-7999 -% e-mail: gray@siam.org - -% -% This is a file of macros and definitions for creating a chapter -% for publication in the SIAM Proceedings Series using Plain TeX. - -% Report the version. -\message{*** SIAM Plain TeX Proceedings Series macro package, version 1.0, -November 6, 1992.***} - -% Make the @ sign a letter for internal control sequences. -\catcode`\@=11 -% -% -% - -\overfullrule=0pt -\baselineskip=14truept - - -%%% DIMENSIONS %%% - -\hsize=36truepc -\vsize=55truepc -%\hoffset=.5in -\parindent=18truept -\def\firstpar{\parindent=0pt\global\everypar{\parindent=18truept}} -\parskip=0pt - - -%%% FONTS %%% - -\font\tenrm=cmr10 -\font\tenbf=cmbx10 -\font\tenit=cmti10 -\font\tensmc=cmcsc10 -\def\tenpoint{% - \def\rm{\tenrm}\def\bf{\tenbf}% - \def\it{\tenit}\def\smc{\tensmc} - \textfont0=\tenrm \scriptfont0=\sevenrm - \textfont1=\teni \scriptfont1=\seveni - \textfont2=\tensy \scriptfont2=\sevensy - \textfont3=\tenex \scriptfont3=\tenex -\baselineskip=12pt\rm}% - -\font\ninerm=cmr9 -\font\ninebf=cmbx9 -\font\nineit=cmti9 -\def\ninepoint{% - \def\rm{\ninerm}\def\bf{\ninebf}% - \def\it{\nineit}\baselineskip=11pt\rm}% - -\font\eightrm=cmr8 -\font\eightbf=cmbx8 -\font\eightit=cmti8 -\font\eighti=cmmi8 -\font\eightsy=cmsy8 -\def\eightpoint{% - \def\rm{\eightrm}\def\bf{\eightbf}% - \def\it{\eightit}\def\smc{\eightrm}\baselineskip=10pt\rm% - \textfont0=\eightrm \scriptfont0=\sixrm - \textfont1=\eighti \scriptfont1=\sixi - \textfont2=\eightsy \scriptfont2=\sixsy - \textfont3=\tenex \scriptfont3=\tenex -} - -\font\sixrm=cmr6 -\font\sixbf=cmbx6 -\font\sixi=cmmi6 -\font\sixsmc=cmr5 -\font\sixsy=cmsy6 -\def\sixpoint{% - \def\rm{\sixrm}\def\bf{\sixbf}% - \def\smc{\sixsmc}\baselineskip=8pt\rm}% - -\fontdimen13\tensy=2.6pt -\fontdimen14\tensy=2.6pt -\fontdimen15\tensy=2.6pt -\fontdimen16\tensy=1.2pt -\fontdimen17\tensy=1.2pt -\fontdimen18\tensy=1.2pt - -\font\eightrm=cmr8 -\font\ninerm=cmr9 -\font\elevenrm=cmr10 scaled\magstephalf -\font\fourteenrm=cmr10 scaled\magstep 1 -\font\eighteenrm=cmr10 scaled\magstep 3 -\font\twelvebf=cmbx10 scaled\magstep 1 -\font\elevenbf=cmbx10 scaled\magstephalf -\font\elevenit=cmti10 scaled\magstephalf -\font\elevensc=cmcsc10 scaled\magstephalf - -\def\theoremfont{\elevensc} -\def\textfont{\elevenrm} -\def\itfont{\elevenit} -\def\headfont{\twelvebf} -\def\smallheadfont{\elevenbf} -\def\titlefont{\eighteenrm} -\def\chapterfont{\fourteenrm} -\def\authorfont{\fourteenrm} -\def\rheadfont{\tenrm} -\def\abstractfont{\tenrm} -\def\smc{\tensmc} -\font\eightsmc=cmcsc8 - -\def\footnote#1{\baselineskip=11truept\edef\@sf{\spacefactor\the\spacefactor}#1\@sf - \insert\footins\bgroup\ninepoint\hsize=36pc - \interlinepenalty10000 \let\par=\endgraf - \leftskip=0pt \rightskip=0pt - \splittopskip=10pt plus 1pt minus 1pt \floatingpenalty=20000 -\smallskip -\item{#1}\bgroup\baselineskip=10pt\strut -\aftergroup\@foot\let\next} -\skip\footins=12pt plus 2pt minus 4pt -\dimen\footins=36pc - - - -%%% CHAPTER OPENING MACROS %%% - -\def\startchapter{\topinsert\vglue54pt\endinsert} - -\def\title#1\endtitle{\titlefont\centerline{#1}\vglue5pt}%\vskip40truept\tenrm} -\def\lasttitle#1\endlasttitle{\titlefont\centerline{#1}\vskip1.32truepc} -\def\author#1\endauthor{\authorfont\centerline{#1}\vglue8pt\textfont} -\def\lastauthor#1\endlastauthor{\authorfont\centerline{#1}\vglue2.56pc\textfont} -\def\abstract#1\endabstract{\baselineskip=12pt\leftskip=2.25pc - \rightskip=2.25pc\abstractfont{#1}\textfont} - -%%% COUNTERS FOR HEADINGS %%% - -\newcount\headcount -\headcount=1 -\newcount\seccount -\seccount=1 -\newcount\subseccount -\subseccount=1 -\def\secreset{\global\seccount=1} - \def\subsecreset{\global\subseccount=1} - -%%% HEADINGS %%% - -\def\headone#1{\baselineskip=14pt\leftskip=0pt\rightskip=0pt\vskip17truept\parindent=0pt -{\headfont\the\headcount\hskip14truept #1} -\par\nobreak\firstpar\global\advance\headcount by 0 - \global\advance\headcount by 1\secreset\vskip2truept\textfont} - -\def\headtwo#1{\advance\headcount by -1% - \vskip17truept\parindent=0pt{\headfont\the\headcount.% - \the\seccount\hskip14truept #1}%\enspace\ignorespaces\firstpar - \global\advance\headcount by 1\global\advance\seccount by 1 - \global\advance\subseccount by 1\subsecreset\vskip2pt\textfont} - - \def\headthree#1{\advance\headcount by -1\advance\seccount by -1 -% \advance\subseccount by -1% - \vskip17truept\parindent=0pt{\smallheadfont\the\headcount.% - \the\seccount.\the\subseccount\hskip11truept #1}\hskip6pt\ignorespaces - \firstpar\global\advance\headcount by 1\global\advance\seccount by 1 - \global\advance\subseccount by 1\textfont} - -%%% THEOREMS, PROOFS, DEFINITIONS, etc. %%% - -\def\thm#1{{\theoremfont -#1\enspace} -\hskip-5pt\begingroup\itfont\ignorespaces} - -\let\lem=\thm -\let\cor=\thm -\let\prop=\thm - -\def\endthm{\endgroup\textfont} -\let\endlem=\endthm -\let\endcor=\endthm -\let\endprop=\endthm - -\def\prf#1{{\itfont #1.}\textfont\enspace\ignorespaces} -\let\rem=\prf -\let\case=\prf - -\def\endprf{\textfont} -\let\endrem=\endprf -\let\endcase=\endprf - -\def\qed{{\qquad \vbox{\hrule\hbox{% - \vrule height1.3ex\hskip0.8ex\vrule}\hrule - }}\par} - -\def\dfn#1{{\theoremfont -#1\enspace} -\textfont\ignorespaces} - -\let\fact=\dfn - -\def\enddfn{\textfont} - -\let\endfact=\enddfn - -%%% FIGURES AND CAPTIONS %%% - - -\newcount\figcount -\figcount=1 - - -%\newcount\tablenumber -%\tablenumber=1 - -\def\\{\hfill\break} - -\newbox\TestBox -\newdimen\setwd -\newskip\belowcaptionskip -\belowcaptionskip=6pt plus 1pt - -\def\endinsert{\egroup % finish the \vbox - \if@mid \dimen@\ht\z@ \advance\dimen@\dp\z@ - \advance\dimen@12\p@ \advance\dimen@\pagetotal - \ifdim\dimen@>\pagegoal\@midfalse\p@gefalse\fi\fi - \if@mid\vskip\belowcaptionskip\box\z@\par \penalty-200\vskip\belowcaptionskip - \else\insert\topins{\penalty100 % floating insertion - \splittopskip\z@skip - \splitmaxdepth\maxdimen \floatingpenalty\z@ - \ifp@ge \dimen@\dp\z@ - \vbox to\vsize{\unvbox\z@\kern-\dimen@}% depth is zero - \else \box\z@\nobreak\vskip\belowcaptionskip\fi}\fi\endgroup} - - - - -\def\fig#1#2#3{% - \setbox\TestBox=\hbox{\tenpoint #3.}\setwd=\wd\TestBox - \topinsert - \vskip #1 - \vskip 12pt - \ifdim\setwd > 23pc - {\tenit{\smc #2.}\ \ #3} - \else - \centerline{\tenit\noindent - {\smc #2.}\ \ #3}\fi% - % \global\advance\figcount by 1 - \endinsert} - - - -%%% REFERENCES %%% - -\newdimen\refindent@ -\newdimen\refhangindent@ -\newbox\refbox@ -\setbox\refbox@=\hbox{\tenrm\baselineskip=11pt [00]}% Default 2 digits -\refindent@=\wd\refbox@ - -\def\resetrefindent#1{% - \setbox\refbox@=\hbox{\tenrm\baselineskip=11pt [#1]}% - \refindent@=\wd\refbox@} - -\def\Refs{% - \unskip\vskip1pc - \leftline{\noindent\headfont References}% - \penalty10000 - \vskip4pt - \penalty10000 - \refhangindent@=\refindent@ - \global\advance\refhangindent@ by .5em - \global\everypar{\hangindent\refhangindent@}% - \parindent=0pt\baselineskip=12pt\tenrm} - -\def\sameauthor{\leavevmode\vbox to 1ex{\vskip 0pt plus 100pt - \hbox to 2em{\leaders\hrule\hfil}\vskip 0pt plus 300pt}} - -\def\ref#1\\#2\endref{\leavevmode\hbox to \refindent@{\hfil[#1]}\enspace #2\par} - - -%%% OUTPUT %%% - -\def\rightheadline{\hfill\tensmc\rightrh\hskip2pc\tenrm\folio} -\def\leftheadline{\tenrm\folio\hskip2pc\tensmc\leftrh\hfill} - -\global\footline={\hss\tenrm\folio\hss}% first page - -\output{\plainoutput} -\def\plainoutput{\shipout\vbox{\makeheadline\pagebody\makefootline}% - \advancepageno - \ifnum\pageno>1 - \global\footline={\hfill}% - \fi - \ifodd\pageno - \global\headline={\rightheadline}% - \else - \global\headline={\leftheadline}% - \fi - \ifnum\outputpenalty>-\@MM \else\dosupereject\fi} -\def\pagebody{\vbox to\vsize{\boxmaxdepth\maxdepth \pagecontents}} -\def\makeheadline{\vbox to\z@{\vskip-22.5\p@ - \line{\vbox to8.5\p@{}\rheadfont\the\headline}\vss}% - \nointerlineskip} -\def\makefootline{\baselineskip24\p@\vskip-6\p@\line{\the\footline}} -\def\dosupereject{\ifnum\insertpenalties>\z@ % something is being held over - \line{}\kern-\topskip\nobreak\vfill\supereject\fi} - -\def\footnoterule{\vskip11pt\kern -4\p@\hrule width 3pc \kern 3.6\p@ } % rule = .4 pt high - -% Turn off @ as being a letter. -% -\catcode`\@=13 - -%end of style file diff --git a/Master/texmf-dist/source/latex/siam/soda209.all b/Master/texmf-dist/source/latex/siam/soda209.all deleted file mode 100644 index 862535ccfd3..00000000000 --- a/Master/texmf-dist/source/latex/siam/soda209.all +++ /dev/null @@ -1,682 +0,0 @@ -%% This is soda209.all. This file is to be used for creating a paper -%% in the ACM/SIAM Preprint series with LaTeX. It consists of the following -%% two files: -%% -%% ltexprt.tex ---- an example and documentation file -%% ltexprt.sty ---- the macro file -%% -%% To use, cut this file apart at the appropriate places. You can run the -%% example file with the macros to get sample output. -%% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%% CUT HERE %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% -% -%%%%%%%%%%%%%%%%%%%%%%%%%% ltexprt.tex %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% -% This is ltexprt.tex, an example file for use with the SIAM LaTeX (version 2.09) -% Preprint Series macros. It is designed to provide double-column output. -% Please take the time to read the following comments, as they document -% how to use these macros. This file can be composed and printed out for -% use as sample output. - -% Any comments or questions regarding these macros should be directed to: -% -% Corey Gray -% SIAM -% 3600 University City Science Center -% Philadelphia, PA 19104-2688 -% USA -% Telephone: (215) 382-9800 -% Fax: (215) 386-7999 -% e-mail: gray@siam.org - - -% This file is to be used as an example for style only. It should not be read -% for content. - -%%%%%%%%%%%%%%% PLEASE NOTE THE FOLLOWING STYLE RESTRICTIONS %%%%%%%%%%%%%%% - -%% 1. There are no new tags. Existing LaTeX tags have been formatted to match -%% the Preprint series style. -%% -%% 2. You must use \cite in the text to mark your reference citations and -%% \bibitem in the listing of references at the end of your chapter. See -%% the examples in the following file. If you are using BibTeX, please -%% supply the bst file with the manuscript file. -%% -%% -%% 3. This macro is set up for two levels of headings (\section and -%% \subsection). The macro will automatically number the headings for you. -%% -%% 4. No running heads are to be used in this volume. -%% -%% 5. Theorems, Lemmas, Definitions, etc. are to be double numbered, -%% indicating the section and the occurence of that element -%% within that section. (For example, the first theorem in the second -%% section would be numbered 2.1. The macro will -%% automatically do the numbering for you. -%% -%% 6. Figures, equations, and tables must be single-numbered. -%% Use existing LaTeX tags for these elements. -%% Numbering will be done automatically. -%% -%% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - - - -\documentstyle[twoside,leqno,twocolumn,ltexprt]{article} - -\begin{document} - - -\title{\Large SIAM/ACM Preprint Series Macros for -Use With LaTeX\thanks{Supported by GSF grants ABC123, DEF456, and GHI789.}} -\author{Corey Gray\thanks{Society for Industrial and Applied Mathematics.} \\ -\and -Tricia Manning\thanks{Society for Industrial and Applied Mathematics.}} -\date{} - -\maketitle - -\pagestyle{myheadings} -\markboth{}{} - -%\pagenumbering{arabic} - - -\begin{abstract} \small\baselineskip=9pt This is the text of my abstract. It is a brief -description of my -paper, outlining the purposes and goals I am trying to address.\end{abstract} - -\section{Problem Specification.}In this paper, we consider the solution of the $N \times -N$ linear -system -\begin{equation} \label{e1.1} -A x = b -\end{equation} -where $A$ is large, sparse, symmetric, and positive definite. We consider -the direct solution of (\ref{e1.1}) by means of general sparse Gaussian -elimination. In such a procedure, we find a permutation matrix $P$, and -compute the decomposition -\[ -P A P^{t} = L D L^{t} -\] -where $L$ is unit lower triangular and $D$ is diagonal. - - -\section{Design Considerations.}Several good ordering algorithms (nested dissection and -minimum degree) -are available for computing $P$ \cite{GEORGELIU}, \cite{ROSE72}. -Since our interest here does not -focus directly on the ordering, we assume for convenience that $P=I$, -or that $A$ has been preordered to reflect an appropriate choice of $P$. - -Our purpose here is to examine the nonnumerical complexity of the -sparse elimination algorithm given in \cite{BANKSMITH}. -As was shown there, a general sparse elimination scheme based on the -bordering algorithm requires less storage for pointers and -row/column indices than more traditional implementations of general -sparse elimination. This is accomplished by exploiting the m-tree, -a particular spanning tree for the graph of the filled-in matrix. - -\begin{theorem} The method was extended to three -dimensions. For the standard multigrid -coarsening -(in which, for a given grid, the next coarser grid has $1/8$ -as many points), anisotropic problems require plane -relaxation to -obtain a good smoothing factor.\end{theorem} - -Our purpose here is to examine the nonnumerical complexity of the -sparse elimination algorithm given in \cite{BANKSMITH}. -As was shown there, a general sparse elimination scheme based on the -bordering algorithm requires less storage for pointers and -row/column indices than more traditional implementations of general -sparse elimination. This is accomplished by exploiting the m-tree, -a particular spanning tree for the graph of the filled-in matrix. -Several good ordering algorithms (nested dissection and minimum degree) -are available for computing $P$ \cite{GEORGELIU}, \cite{ROSE72}. -Since our interest here does not -focus directly on the ordering, we assume for convenience that $P=I$, -or that $A$ has been preordered to reflect an appropriate choice of $P$. - -\begin{proof} In this paper we consider two methods. The first method -is -basically the method considered with two differences: -first, we perform plane relaxation by a two-dimensional -multigrid method, and second, we use a slightly different -choice of -interpolation operator, which improves performance -for nearly singular problems. In the second method coarsening -is done by successively coarsening in each of the three -independent variables and then ignoring the intermediate -grids; this artifice simplifies coding considerably. -\end{proof} - -Our purpose here is to examine the nonnumerical complexity of the -sparse elimination algorithm given in \cite{BANKSMITH}. -As was shown there, a general sparse elimination scheme based on the -bordering algorithm requires less storage for pointers and -row/column indices than more traditional implementations of general -sparse elimination. This is accomplished by exploiting the m-tree, -a particular spanning tree for the graph of the filled-in matrix. - -\begin{Definition}{\rm We describe the two methods in \S 1.2. In \S\ 1.3. we -discuss -some remaining details.} -\end{Definition} - -Our purpose here is to examine the nonnumerical complexity of the -sparse elimination algorithm given in \cite{BANKSMITH}. -As was shown there, a general sparse elimination scheme based on the -bordering algorithm requires less storage for pointers and -row/column indices than more traditional implementations of general -sparse elimination. This is accomplished by exploiting the m-tree, -a particular spanning tree for the graph of the filled-in matrix. -Several good ordering algorithms (nested dissection and minimum degree) -are available for computing $P$ \cite{GEORGELIU}, \cite{ROSE72}. -Since our interest here does not -focus directly on the ordering, we assume for convenience that $P=I$, -or that $A$ has been preordered to reflect an appropriate choice of $P$. - -Our purpose here is to examine the nonnumerical complexity of the -sparse elimination algorithm given in \cite{BANKSMITH}. -As was shown there, a general sparse elimination scheme based on the -bordering algorithm requires less storage for pointers and -row/column indices than more traditional implementations of general -sparse elimination. - -\begin{lemma} We discuss first the choice for $I_{k-1}^k$ -which is a generalization. We assume that $G^{k-1}$ is -obtained -from $G^k$ -by standard coarsening; that is, if $G^k$ is a tensor product -grid $G_{x}^k \times G_{y}^k \times G_{z}^k$, -$G^{k-1}=G_{x}^{k-1} \times G_{y}^{k-1} \times G_{z}^{k-1}$, -where $G_{x}^{k-1}$ is obtained by deleting every other grid -point of $G_x^k$ and similarly for $G_{y}^k$ and $G_{z}^k$. -\end{lemma} - -To our knowledge, the m-tree previously has not been applied in this -fashion to the numerical factorization, but it has been used, -directly or indirectly, in several optimal order algorithms for -computing the fill-in during the symbolic factorization phase -[4] - [10], [5], [6]. In \S 1.3., we analyze the complexity of the old and new -approaches to the intersection problem for the special case of -an $n \times n$ grid ordered by nested dissection. The special -structure of this problem allows us to make exact estimates of -the complexity. To our knowledge, the m-tree previously has not been applied in this -fashion to the numerical factorization, but it has been used, -directly or indirectly, in several optimal order algorithms for -computing the fill-in during the symbolic factorization phase -[4] - [10], [5], [6]. - -In \S 1.2, we review the bordering algorithm, and introduce -the sorting and intersection problems that arise in the -sparse formulation of the algorithm. -In \S 1.3., we analyze the complexity of the old and new -approaches to the intersection problem for the special case of -an $n \times n$ grid ordered by nested dissection. The special -structure of this problem allows us to make exact estimates of -the complexity. To our knowledge, the m-tree previously has not been applied in this -fashion to the numerical factorization, but it has been used, -directly or indirectly, in several optimal order algorithms for -computing the fill-in during the symbolic factorization phase -[4] - [10], [5], [6]. - - -For the old approach, we show that the -complexity of the intersection problem is $O(n^{3})$, the same -as the complexity of the numerical computations. For the -new approach, the complexity of the second part is reduced to -$O(n^{2} (\log n)^{2})$. - -To our knowledge, the m-tree previously has not been applied in this -fashion to the numerical factorization, but it has been used, -directly or indirectly, in several optimal order algorithms for -computing the fill-in during the symbolic factorization phase -[4] - [10], [5], [6]. In \S 1.3., we analyze the complexity of the old and new -approaches to the intersection problem for the special case of -an $n \times n$ grid ordered by nested dissection. The special -structure of this problem allows us to make exact estimates of -the complexity. To our knowledge, the m-tree previously has not been applied in this -fashion to the numerical factorization, but it has been used, -directly or indirectly, in several optimal order algorithms for -computing the fill-in during the symbolic factorization phase -[4] - [10], [5], [6]. -This is accomplished by exploiting the m-tree, -a particular spanning tree for the graph of the filled-in matrix. -To our knowledge, the m-tree previously has not been applied in this -fashion to the numerical factorization, but it has been used, -directly or indirectly, in several optimal order algorithms for -computing the fill-in during the symbolic factorization phase -\cite{EISENSTAT} - \cite{LIU2}, \cite{ROSE76}, \cite{SCHREIBER}. - -\subsection{Robustness.}\ We do not -attempt to present an overview -here, but rather attempt to focus on those results that -are relevant to our particular algorithm. -This section assumes prior knowledge of the role of graph theory -in sparse Gaussian elimination; surveys of this role are -available in \cite{ROSE72} and \cite{GEORGELIU}. More general -discussions of elimination trees are given in -\cite{LAW} - \cite{LIU2}, \cite{SCHREIBER}. -Thus, at the $k$th stage, the bordering algorithm consists of -solving the lower triangular system -\begin{equation} \label{1.2} - L_{k-1}v = c -\end{equation} -and setting -\begin{eqnarray} -\ell &=& D^{-1}_{k-1}v , \\ -\delta &=& \alpha - \ell^{t} v . -\end{eqnarray} - -\begin{figure} -\vspace{14pc} -\caption{This is a figure 1.1.} -\end{figure} - -\section{Robustness.} We do not -attempt to present an overview -here, but rather attempt to focus on those results that -are relevant to our particular algorithm. - -\subsection{Versatility.}\ The special -structure of this problem allows us to make exact estimates of -the complexity. For the old approach, we show that the -complexity of the intersection problem is $O(n^{3})$, the same -as the complexity of the numerical computations -\cite{GEORGELIU}, \cite{ROSEWHITTEN}. For the -new approach, the complexity of the second part is reduced to -$O(n^{2} (\log n)^{2})$. - -To our knowledge, the m-tree previously has not been applied in this -fashion to the numerical factorization, but it has been used, -directly or indirectly, in several optimal order algorithms for -computing the fill-in during the symbolic factorization phase -[4] - [10], [5], [6]. In \S 1.3., we analyze the complexity of the old and new -approaches to the intersection problem for the special case of -an $n \times n$ grid ordered by nested dissection. The special -structure of this problem allows us to make exact estimates of -the complexity. To our knowledge, the m-tree previously has not been applied in this -fashion to the numerical factorization, but it has been used, -directly or indirectly, in several optimal order algorithms for -computing the fill-in during the symbolic factorization phase -[4] - [10], [5], [6]. - -In \S 1.2, we review the bordering algorithm, and introduce -the sorting and intersection problems that arise in the -sparse formulation of the algorithm. -In \S 1.3., we analyze the complexity of the old and new -approaches to the intersection problem for the special case of -an $n \times n$ grid ordered by nested dissection. The special -structure of this problem allows us to make exact estimates of -the complexity. To our knowledge, the m-tree previously has not been applied in this -fashion to the numerical factorization, but it has been used, -directly or indirectly, in several optimal order algorithms for -computing the fill-in during the symbolic factorization phase -[4] - [10], [5], [6]. - - -For the old approach, we show that the -complexity of the intersection problem is $O(n^{3})$, the same -as the complexity of the numerical computations. For the -new approach, the complexity of the second part is reduced to -$O(n^{2} (\log n)^{2})$. - -To our knowledge, the m-tree previously has not been applied in this -fashion to the numerical factorization, but it has been used, -directly or indirectly, in several optimal order algorithms for -computing the fill-in during the symbolic factorization phase -[4] - [10], [5], [6]. In \S 1.3., we analyze the complexity of the old and new -approaches to the intersection problem for the special case of -an $n \times n$ grid ordered by nested dissection. The special -structure of this problem allows us to make exact estimates of -the complexity. To our knowledge, the m-tree previously has not been applied in this -fashion to the numerical factorization, but it has been used, -directly or indirectly, in several optimal order algorithms for -computing the fill-in during the symbolic factorization phase -[4] - [10], [5], [6]. -This is accomplished by exploiting the m-tree, -a particular spanning tree for the graph of the filled-in matrix. -To our knowledge, the m-tree previously has not been applied in this -fashion to the numerical factorization, but it has been used, -directly or indirectly, in several optimal order algorithms for -computing the fill-in during the symbolic factorization phase -\cite{EISENSTAT} - \cite{LIU2}, \cite{ROSE76}, \cite{SCHREIBER}. - -\begin{thebibliography}{99} - -%\bibitem{GUIDE} -%R.~E. Bank, {\em PLTMG users' guide, edition 5.0}, tech. report, -% Department of Mathematics, University of California, San Diego, CA, 1988. - -%\bibitem{HBMG} -%R.~E. Bank, T.~F. Dupont, and H.~Yserentant, {\em The hierarchical basis -% multigrid method}, Numer. Math., 52 (1988), pp.~427--458. - -\bibitem{BANKSMITH} -R.~E. Bank and R.~K. Smith, {\em General sparse elimination requires no - permanent integer storage}, SIAM J. Sci. Stat. Comput., 8 (1987), - pp.~574--584. - -\bibitem{EISENSTAT} -S.~C. Eisenstat, M.~C. Gursky, M.~Schultz, and A.~Sherman, {\em - Algorithms and data structures for sparse symmetric gaussian elimination}, - SIAM J. Sci. Stat. Comput., 2 (1982), pp.~225--237. - -\bibitem{GEORGELIU} -A.~George and J.~Liu, {\em Computer Solution of Large Sparse Positive - Definite Systems}, Prentice Hall, Englewood Cliffs, NJ, 1981. - -\bibitem{LAW} -K.~H. Law and S.~J. Fenves, {\em A node addition model for symbolic - factorization}, ACM TOMS, 12 (1986), pp.~37--50. - -\bibitem{LIU} -J.~W.~H. Liu, {\em A compact row storage scheme for cholesky factors - using elimination trees}, ACM TOMS, 12 (1986), pp.~127--148. - -\bibitem{LIU2} -\sameauthor , {\em The role of - elimination trees in sparse factorization}, Tech. Report CS-87-12,Department - of Computer Science, York University, Ontario, Canada, 1987. - -\bibitem{ROSE72} -D.~J. Rose, {\em A graph theoretic study of the numeric solution of - sparse positive definite systems}, in Graph Theory and Computing, AcademicΠPress, New -York, 1972. - -\bibitem{ROSE76} -D.~J. Rose, R.~E. Tarjan, and G.~S. Lueker, {\em Algorithmic aspects of - vertex elimination on graphs}, SIAM J. Comput., 5 (1976), pp.~226--283. - -\bibitem{ROSEWHITTEN} -D.~J. Rose and G.~F. Whitten, {\em A recursive analysis of disection - strategies}, in Sparse Matrix Computations, Academic Press, New York, 1976. - -\bibitem{SCHREIBER} -R.~Schrieber, {\em A new implementation of sparse gaussian elimination}, - ACM TOMS, 8 (1982), pp.~256--276. - -\end{thebibliography} -\end{document} - -% End of ltexprt.tex -% -% -% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% CUT HERE %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% -% -% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% ltexprt.sty %%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% -% This is ltexprt.sty, a file of macros and definitions for creating a -% chapter for publication in the ACM/SIAM Preprint series using LaTeX (version 2.09). -% It is designed to produce double-column output. -% This file may be freely distributed but may not be altered in any way. -% Any comments or questions regarding these macros should be directed to: - -% Corey Gray -% SIAM -% 3600 University City Science Center -% Philadelphia, PA 19104-2688 -% USA -% Telephone: (215) 382-9800 -% Fax: (215) 386-7999 -% e-mail: gray@siam.org - - -% Report the version. -\message{*** ACM/SIAM LaTeX 2.09 Preprint Series macro package, version 1.0, -September 24,1990 ***} - - -\pretolerance=800 -\tolerance=10000 -\sloppy - -\voffset=-.5in -\hoffset=-.5in -\vsize=55pc -\hsize=41pc -\baselineskip=14pt -\footskip=18pt -\topmargin 24pt -\headheight 12pt -\headsep 17pt -\textheight 52.5pc \advance\textheight by \topskip -\textwidth 41pc -\parskip 0pt -\parindent 18pt - -\font\tensmc=cmcsc10 -\def\smc{\tensmc} - -%% footnotes to be set 8/10 -\def\footnotesize{\@setsize\footnotesize{10pt}\viiipt\@viiipt - % \indent - \abovedisplayskip \z@ - \belowdisplayskip\z@ - \abovedisplayshortskip\abovedisplayskip - \belowdisplayshortskip\belowdisplayshortskip - \def\@listi{\leftmargin\leftmargini \topsep 3pt plus 1pt minus 1pt - \parsep 2pt plus 1pt minus 1pt - \itemsep \parsep}} - -\let\referencesize\footnotesize - -\footnotesep 0pt - -\skip\footins 12pt plus 12pt - -\def\footnoterule{\kern3\p@ \hrule width 3em} % the \hrule is .4pt high - -\def\ps@plain{\let\@mkboth\@gobbletwo - \def\@oddfoot{{\hfil\small\thepage\hfil}}% - \def\@oddhead{} - \def\@evenhead{}\def\@evenfoot{}} - - - - - -\def\ps@headings{\let\@mkboth\markboth - \def\@oddfoot{}\def\@evenfoot{}% - \def\@evenhead{{\rm\thepage}\hfil{\small\leftmark}}% - \def\@oddhead{{\noindent\small\rightmark}\hfil{\rm\thepage}}% - - - -\def\ps@myheadings{\let\@mkboth\@gobbletwo - \def\@oddfoot{}\def\@evenfoot{}% - \def\@oddhead{\rlap{\normalsize\rm\rightmark}\hfil{small\thepage}}% - \def\@evenhead%{\hfil{\small\@chapapp}\ - {\small\thepage}\hfil\llap{\normalsize\rm\leftmark}}% - \def\chaptermark##1{}% - \def\sectionmark##1{}\def\subsectionmark##1{}} - - -\def\theequation{\arabic{section}.\arabic{equation}} - - -\def\section{\@startsection{section}{1}{0pt}{-12pt}{3pt}{\hyphenpenalty=\@M -\exhyphenpenalty=\@M\normalsize\bf}} -\def\subsection{\@startsection{subsection}{2}{0pt}{-12pt}{0pt}{\normalsize\bf} -} -\def\subsubsection{\@startsection - {subsubsection}{3}{0pt}{-12pt}{0pt}{\normalsize\bf}} -\def\paragraph{\@startsection - {paragraph}{4}{\parindent}{0pt}{0pt}{\normalsize\bf}} -\def\subparagraph{\@startsection - {subparagraph}{4}{\parindent}{0pt}{0pt}{\normalsize\bf}} - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% % -% THEOREMS, PROOFS, ALGORITHMS % -% % -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -%%% defined proof environment by theorem model (took out counter) - -\def\newproof#1{\@nprf{#1}} - -\def\@nprf#1#2{\@xnprf{#1}{#2}} - -\def\@xnprf#1#2{\expandafter\@ifdefinable\csname #1\endcsname -\global\@namedef{#1}{\@prf{#1}{#2}}\global\@namedef{end#1}{\@endproof}} - -\def\@prf#1#2{\@xprf{#1}{#2}} - -\def\@xprf#1#2{\@beginproof{#2}{\csname the#1\endcsname}\ignorespaces} - - - -%%% defined algorithm environment by theorem model - -\def\newalgorithm#1{\@ifnextchar[{\@oalg{#1}}{\@nalg{#1}}} - -\def\@nalg#1#2{% -\@ifnextchar[{\@xnalg{#1}{#2}}{\@ynalg{#1}{#2}}} - -\def\@xnalg#1#2[#3]{\expandafter\@ifdefinable\csname #1\endcsname -{\@definecounter{#1}\@addtoreset{#1}{#3}% -\expandafter\xdef\csname the#1\endcsname{\expandafter\noexpand - \csname the#3\endcsname \@thmcountersep \@thmcounter{#1}}% -\global\@namedef{#1}{\@alg{#1}{#2}}\global\@namedef{end#1}{\@endalgorithm}}} - -\def\@ynalg#1#2{\expandafter\@ifdefinable\csname #1\endcsname -{\@definecounter{#1}% -\expandafter\xdef\csname the#1\endcsname{\@thmcounter{#1}}% -\global\@namedef{#1}{\@alg{#1}{#2}}\global\@namedef{end#1}{\@endalgorithm}}} - -\def\@oalg#1[#2]#3{\expandafter\@ifdefinable\csname #1\endcsname - {\global\@namedef{the#1}{\@nameuse{the#2}}% -\global\@namedef{#1}{\@alg{#2}{#3}}% -\global\@namedef{end#1}{\@endalgorithm}}} - -\def\@alg#1#2{\refstepcounter - {#1}\@ifnextchar[{\@yalg{#1}{#2}}{\@xalg{#1}{#2}}} - -\def\@xalg#1#2{\@beginalgorithm{#2}{\csname the#1\endcsname}\ignorespaces} -\def\@yalg#1#2[#3]{\@opargbeginalgorithm{#2}{\csname - the#1\endcsname}{#3}\ignorespaces} - - - - -\def\@beginproof#1{\rm \trivlist \item[\hskip \labelsep{\it #1.\/}]} -\def\@endproof{\outerparskip 0pt\endtrivlist} - -\def\@begintheorem#1#2{\it \trivlist \item[\hskip \labelsep{\sc #1\ #2.}]} -\def\@opargbegintheorem#1#2#3{\it \trivlist - \item[\hskip \labelsep{\sc #1\ #2.\ (#3)}]} -\def\@endtheorem{\outerparskip 0pt\endtrivlist} - -%\def\@begindefinition#1#2{\rm \trivlist \item[\hskip \labelsep{\sc #1\ #2.}]} -%\def\@opargbegindefinition#1#2#3{\rm \trivlist -% \item[\hskip \labelsep{\sc #1\ #2.\ (#3)}]} -%\def\@enddefinition{\outerparskip 0pt\endtrivlist} - - -\def\@beginalgorithm#1#2{\rm \trivlist \item[\hskip \labelsep{\sc #1\ #2.}]} -\def\@opargbeginalgorithm#1#2#3{\rm \trivlist - \item[\hskip \labelsep{\sc #1\ #2.\ (#3)}]} -\def\@endalgorithm{\outerparskip 6pt\endtrivlist} - - -\newskip\outerparskip - -\def\trivlist{\parsep\outerparskip - \@trivlist \labelwidth\z@ \leftmargin\z@ - \itemindent\parindent \def\makelabel##1{##1}} - -\def\@trivlist{\topsep=0pt\@topsepadd\topsep - \if@noskipsec \leavevmode \fi - \ifvmode \advance\@topsepadd\partopsep \else \unskip\par\fi - \if@inlabel \@noparitemtrue \@noparlisttrue - \else \@noparlistfalse \@topsep\@topsepadd \fi - \advance\@topsep \parskip - \leftskip\z@\rightskip\@rightskip \parfillskip\@flushglue - \@setpar{\if@newlist\else{\@@par}\fi}% - \global\@newlisttrue \@outerparskip\parskip} - - -\def\endtrivlist{\if@newlist\@noitemerr\fi - \if@inlabel\indent\fi - \ifhmode\unskip \par\fi - \if@noparlist \else - \ifdim\lastskip >\z@ \@tempskipa\lastskip \vskip -\lastskip - \advance\@tempskipa\parskip \advance\@tempskipa -\@outerparskip - \vskip\@tempskipa - \fi\@endparenv\fi - \vskip\outerparskip} - - - - \newproof{@proof}{Proof} - \newenvironment{proof}{\begin{@proof}}{\end{@proof}} - - \newtheorem{@theorem}{Theorem}[section] - \newenvironment{theorem}{\begin{@theorem}}{\end{@theorem}} - - \newalgorithm{@algorithm}{Algorithm}[section] - \newenvironment{algorithm}{\begin{@algorithm}}{\end{@algorithm}} - - - -\newtheorem{lemma}{Lemma}[section] -\newtheorem{fact}{Fact}[section] -\newtheorem{corollary}{Corollary}[section] -\newtheorem{axiom}{Axiom}[section] -\newtheorem{cond}{Condition}[section] -\newtheorem{property}{Property}[section] -\newtheorem{proposition}{Proposition}[section] - -\newtheorem{Conjecture}{Conjecture}[section] -%\newtheorem{Corollary}[Theorem]{Corollary} -\newtheorem{Definition}{Definition}[section] -\newtheorem{Lemma}{Lemma}[section] -\newtheorem{Remark}{Remark}[section] - -\newproof{Example}{Example} -\newproof{Method}{Method} -\newproof{Exercise}{Exercise} - - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% %% -%% BIBLIOGRAPHY %% -%% %% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - - -\def\thebibliography#1{% -%\cleardoublepage -\parindent 0em -\vspace{6pt} -\begin{flushleft}\normalsize\bf References\end{flushleft} -\addvspace{3pt}\nopagebreak\list - %% default is no labels, for those not using \cite or BibTeX -% {[\arabic{enumi}]} {\settowidth\labelwidth{[#1]} -{[\arabic{enumi}]}{\settowidth\labelwidth{mm} -\leftmargin\labelwidth - \advance\leftmargin\labelsep - \usecounter{enumi}\@bibsetup} -\def\newblock{\hskip .11em plus .33em minus -.07em} - \sloppy\clubpenalty4000\widowpenalty4000 - \sfcode`\.=1000\relax} - -%% setup 8/10 type -\def\@bibsetup{\itemindent=0pt \itemsep=0pt \parsep=0pt -\small} - -\def\sameauthor{\leavevmode\vrule height 2pt depth -1.6pt width 23pt} - -% -%% End of ltexprt.sty -% -%%%%%%%%%%%%%%%%%%%%%%%%% End of soda209.all %%%%%%%%%%%%%%%%%%%%%%% diff --git a/Master/texmf-dist/source/latex/siam/soda2e.all b/Master/texmf-dist/source/latex/siam/soda2e.all deleted file mode 100644 index 17f570966fa..00000000000 --- a/Master/texmf-dist/source/latex/siam/soda2e.all +++ /dev/null @@ -1,688 +0,0 @@ -%% This is soda2e.all. This file is to be used for creating a paper -%% in the ACM/SIAM Preprint series with LaTeX2E. It consists of the following -%% two files: -%% -%% ltexpprt.tex ---- an example and documentation file -%% ltexpprt.sty ---- the macro file -%% -%% To use, cut this file apart at the appropriate places. You can run the -%% example file with the macros to get sample output. -%% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%% CUT HERE %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% -% -%%%%%%%%%%%%%%%%%%%%%%%%%% ltexpprt.tex %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% -% This is ltexpprt.tex, an example file for use with the SIAM LaTeX2E -% Preprint Series macros. It is designed to provide double-column output. -% Please take the time to read the following comments, as they document -% how to use these macros. This file can be composed and printed out for -% use as sample output. - -% Any comments or questions regarding these macros should be directed to: -% -% Corey Gray -% SIAM -% 3600 University City Science Center -% Philadelphia, PA 19104-2688 -% USA -% Telephone: (215) 382-9800 -% Fax: (215) 386-7999 -% e-mail: gray@siam.org - - -% This file is to be used as an example for style only. It should not be read -% for content. - -%%%%%%%%%%%%%%% PLEASE NOTE THE FOLLOWING STYLE RESTRICTIONS %%%%%%%%%%%%%%% - -%% 1. There are no new tags. Existing LaTeX tags have been formatted to match -%% the Preprint series style. -%% -%% 2. You must use \cite in the text to mark your reference citations and -%% \bibitem in the listing of references at the end of your chapter. See -%% the examples in the following file. If you are using BibTeX, please -%% supply the bst file with the manuscript file. -%% -%% 3. This macro is set up for two levels of headings (\section and -%% \subsection). The macro will automatically number the headings for you. -%% -%% 5. No running heads are to be used for this volume. -%% -%% 6. Theorems, Lemmas, Definitions, etc. are to be double numbered, -%% indicating the section and the occurence of that element -%% within that section. (For example, the first theorem in the second -%% section would be numbered 2.1. The macro will -%% automatically do the numbering for you. -%% -%% 7. Figures, equations, and tables must be single-numbered. -%% Use existing LaTeX tags for these elements. -%% Numbering will be done automatically. -%% -%% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - - - -\documentclass[twoside,leqno,twocolumn]{article} -\usepackage{ltexpprt} -\begin{document} - - -%\setcounter{chapter}{2} % If you are doing your chapter as chapter one, -%\setcounter{section}{3} % comment these two lines out. - -\title{\Large SIAM/ACM Preprint Series Macros for -Use With LaTeX\thanks{Supported by GSF grants ABC123, DEF456, and GHI789.}} -\author{Corey Gray\thanks{Society for Industrial and Applied Mathematics.} \\ -\and -Tricia Manning\thanks{Society for Industrial and Applied Mathematics.}} -\date{} - -\maketitle - -\pagestyle{myheadings} -\markboth{}{} - - -%\pagenumbering{arabic} -%\setcounter{page}{1}%Leave this line commented out. - -\begin{abstract} \small\baselineskip=9pt This is the text of my abstract. It is a brief -description of my -paper, outlining the purposes and goals I am trying to address.\end{abstract} - - - - -\section{Problem Specification.}In this paper, we consider the solution of the $N \times -N$ linear -system -\begin{equation} \label{e1.1} -A x = b -\end{equation} -where $A$ is large, sparse, symmetric, and positive definite. We consider -the direct solution of (\ref{e1.1}) by means of general sparse Gaussian -elimination. In such a procedure, we find a permutation matrix $P$, and -compute the decomposition -\[ -P A P^{t} = L D L^{t} -\] -where $L$ is unit lower triangular and $D$ is diagonal. - - -\section{Design Considerations.}Several good ordering algorithms (nested dissection and -minimum degree) -are available for computing $P$ \cite{GEORGELIU}, \cite{ROSE72}. -Since our interest here does not -focus directly on the ordering, we assume for convenience that $P=I$, -or that $A$ has been preordered to reflect an appropriate choice of $P$. - -Our purpose here is to examine the nonnumerical complexity of the -sparse elimination algorithm given in \cite{BANKSMITH}. -As was shown there, a general sparse elimination scheme based on the -bordering algorithm requires less storage for pointers and -row/column indices than more traditional implementations of general -sparse elimination. This is accomplished by exploiting the m-tree, -a particular spanning tree for the graph of the filled-in matrix. - -\begin{theorem} The method was extended to three -dimensions. For the standard multigrid -coarsening -(in which, for a given grid, the next coarser grid has $1/8$ -as many points), anisotropic problems require plane -relaxation to -obtain a good smoothing factor.\end{theorem} - -Our purpose here is to examine the nonnumerical complexity of the -sparse elimination algorithm given in \cite{BANKSMITH}. -As was shown there, a general sparse elimination scheme based on the -bordering algorithm requires less storage for pointers and -row/column indices than more traditional implementations of general -sparse elimination. This is accomplished by exploiting the m-tree, -a particular spanning tree for the graph of the filled-in matrix. -Several good ordering algorithms (nested dissection and minimum degree) -are available for computing $P$ \cite{GEORGELIU}, \cite{ROSE72}. -Since our interest here does not -focus directly on the ordering, we assume for convenience that $P=I$, -or that $A$ has been preordered to reflect an appropriate choice of $P$. - -\begin{proof} In this paper we consider two methods. The first method -is -basically the method considered with two differences: -first, we perform plane relaxation by a two-dimensional -multigrid method, and second, we use a slightly different -choice of -interpolation operator, which improves performance -for nearly singular problems. In the second method coarsening -is done by successively coarsening in each of the three -independent variables and then ignoring the intermediate -grids; this artifice simplifies coding considerably. -\end{proof} - -Our purpose here is to examine the nonnumerical complexity of the -sparse elimination algorithm given in \cite{BANKSMITH}. -As was shown there, a general sparse elimination scheme based on the -bordering algorithm requires less storage for pointers and -row/column indices than more traditional implementations of general -sparse elimination. This is accomplished by exploiting the m-tree, -a particular spanning tree for the graph of the filled-in matrix. - -\begin{Definition}{\rm We describe the two methods in \S 1.2. In \S\ 1.3. we -discuss -some remaining details.} -\end{Definition} - -Our purpose here is to examine the nonnumerical complexity of the -sparse elimination algorithm given in \cite{BANKSMITH}. -As was shown there, a general sparse elimination scheme based on the -bordering algorithm requires less storage for pointers and -row/column indices than more traditional implementations of general -sparse elimination. This is accomplished by exploiting the m-tree, -a particular spanning tree for the graph of the filled-in matrix. -Several good ordering algorithms (nested dissection and minimum degree) -are available for computing $P$ \cite{GEORGELIU}, \cite{ROSE72}. -Since our interest here does not -focus directly on the ordering, we assume for convenience that $P=I$, -or that $A$ has been preordered to reflect an appropriate choice of $P$. - -Our purpose here is to examine the nonnumerical complexity of the -sparse elimination algorithm given in \cite{BANKSMITH}. -As was shown there, a general sparse elimination scheme based on the -bordering algorithm requires less storage for pointers and -row/column indices than more traditional implementations of general -sparse elimination. - -\begin{lemma} We discuss first the choice for $I_{k-1}^k$ -which is a generalization. We assume that $G^{k-1}$ is -obtained -from $G^k$ -by standard coarsening; that is, if $G^k$ is a tensor product -grid $G_{x}^k \times G_{y}^k \times G_{z}^k$, -$G^{k-1}=G_{x}^{k-1} \times G_{y}^{k-1} \times G_{z}^{k-1}$, -where $G_{x}^{k-1}$ is obtained by deleting every other grid -point of $G_x^k$ and similarly for $G_{y}^k$ and $G_{z}^k$. -\end{lemma} - -To our knowledge, the m-tree previously has not been applied in this -fashion to the numerical factorization, but it has been used, -directly or indirectly, in several optimal order algorithms for -computing the fill-in during the symbolic factorization phase -[4] - [10], [5], [6]. In \S 1.3., we analyze the complexity of the old and new -approaches to the intersection problem for the special case of -an $n \times n$ grid ordered by nested dissection. The special -structure of this problem allows us to make exact estimates of -the complexity. To our knowledge, the m-tree previously has not been applied in this -fashion to the numerical factorization, but it has been used, -directly or indirectly, in several optimal order algorithms for -computing the fill-in during the symbolic factorization phase -[4] - [10], [5], [6]. - -In \S 1.2, we review the bordering algorithm, and introduce -the sorting and intersection problems that arise in the -sparse formulation of the algorithm. -In \S 1.3., we analyze the complexity of the old and new -approaches to the intersection problem for the special case of -an $n \times n$ grid ordered by nested dissection. The special -structure of this problem allows us to make exact estimates of -the complexity. To our knowledge, the m-tree previously has not been applied in this -fashion to the numerical factorization, but it has been used, -directly or indirectly, in several optimal order algorithms for -computing the fill-in during the symbolic factorization phase -[4] - [10], [5], [6]. - - -For the old approach, we show that the -complexity of the intersection problem is $O(n^{3})$, the same -as the complexity of the numerical computations. For the -new approach, the complexity of the second part is reduced to -$O(n^{2} (\log n)^{2})$. - -To our knowledge, the m-tree previously has not been applied in this -fashion to the numerical factorization, but it has been used, -directly or indirectly, in several optimal order algorithms for -computing the fill-in during the symbolic factorization phase -[4] - [10], [5], [6]. In \S 1.3., we analyze the complexity of the old and new -approaches to the intersection problem for the special case of -an $n \times n$ grid ordered by nested dissection. The special -structure of this problem allows us to make exact estimates of -the complexity. To our knowledge, the m-tree previously has not been applied in this -fashion to the numerical factorization, but it has been used, -directly or indirectly, in several optimal order algorithms for -computing the fill-in during the symbolic factorization phase -[4] - [10], [5], [6]. -This is accomplished by exploiting the m-tree, -a particular spanning tree for the graph of the filled-in matrix. -To our knowledge, the m-tree previously has not been applied in this -fashion to the numerical factorization, but it has been used, -directly or indirectly, in several optimal order algorithms for -computing the fill-in during the symbolic factorization phase -\cite{EISENSTAT} - \cite{LIU2}, \cite{ROSE76}, \cite{SCHREIBER}. - -\subsection{Robustness.}\ We do not -attempt to present an overview -here, but rather attempt to focus on those results that -are relevant to our particular algorithm. -This section assumes prior knowledge of the role of graph theory -in sparse Gaussian elimination; surveys of this role are -available in \cite{ROSE72} and \cite{GEORGELIU}. More general -discussions of elimination trees are given in -\cite{LAW} - \cite{LIU2}, \cite{SCHREIBER}. -Thus, at the $k$th stage, the bordering algorithm consists of -solving the lower triangular system -\begin{equation} \label{1.2} - L_{k-1}v = c -\end{equation} -and setting -\begin{eqnarray} -\ell &=& D^{-1}_{k-1}v , \\ -\delta &=& \alpha - \ell^{t} v . -\end{eqnarray} - -\begin{figure} -\vspace{14pc} -\caption{This is a figure 1.1.} -\end{figure} - -\section{Robustness.} We do not -attempt to present an overview -here, but rather attempt to focus on those results that -are relevant to our particular algorithm. - -\subsection{Versatility.}\ The special -structure of this problem allows us to make exact estimates of -the complexity. For the old approach, we show that the -complexity of the intersection problem is $O(n^{3})$, the same -as the complexity of the numerical computations -\cite{GEORGELIU}, \cite{ROSEWHITTEN}. For the -new approach, the complexity of the second part is reduced to -$O(n^{2} (\log n)^{2})$. - -To our knowledge, the m-tree previously has not been applied in this -fashion to the numerical factorization, but it has been used, -directly or indirectly, in several optimal order algorithms for -computing the fill-in during the symbolic factorization phase -[4] - [10], [5], [6]. In \S 1.3., we analyze the complexity of the old and new -approaches to the intersection problem for the special case of -an $n \times n$ grid ordered by nested dissection. The special -structure of this problem allows us to make exact estimates of -the complexity. To our knowledge, the m-tree previously has not been applied in this -fashion to the numerical factorization, but it has been used, -directly or indirectly, in several optimal order algorithms for -computing the fill-in during the symbolic factorization phase -[4] - [10], [5], [6]. - -In \S 1.2, we review the bordering algorithm, and introduce -the sorting and intersection problems that arise in the -sparse formulation of the algorithm. -In \S 1.3., we analyze the complexity of the old and new -approaches to the intersection problem for the special case of -an $n \times n$ grid ordered by nested dissection. The special -structure of this problem allows us to make exact estimates of -the complexity. To our knowledge, the m-tree previously has not been applied in this -fashion to the numerical factorization, but it has been used, -directly or indirectly, in several optimal order algorithms for -computing the fill-in during the symbolic factorization phase -[4] - [10], [5], [6]. - - -For the old approach, we show that the -complexity of the intersection problem is $O(n^{3})$, the same -as the complexity of the numerical computations. For the -new approach, the complexity of the second part is reduced to -$O(n^{2} (\log n)^{2})$. - -To our knowledge, the m-tree previously has not been applied in this -fashion to the numerical factorization, but it has been used, -directly or indirectly, in several optimal order algorithms for -computing the fill-in during the symbolic factorization phase -[4] - [10], [5], [6]. In \S 1.3., we analyze the complexity of the old and new -approaches to the intersection problem for the special case of -an $n \times n$ grid ordered by nested dissection. The special -structure of this problem allows us to make exact estimates of -the complexity. To our knowledge, the m-tree previously has not been applied in this -fashion to the numerical factorization, but it has been used, -directly or indirectly, in several optimal order algorithms for -computing the fill-in during the symbolic factorization phase -[4] - [10], [5], [6]. -This is accomplished by exploiting the m-tree, -a particular spanning tree for the graph of the filled-in matrix. -To our knowledge, the m-tree previously has not been applied in this -fashion to the numerical factorization, but it has been used, -directly or indirectly, in several optimal order algorithms for -computing the fill-in during the symbolic factorization phase -\cite{EISENSTAT} - \cite{LIU2}, \cite{ROSE76}, \cite{SCHREIBER}. - -\begin{thebibliography}{99} - -%\bibitem{GUIDE} -%R.~E. Bank, {\em PLTMG users' guide, edition 5.0}, tech. report, -% Department of Mathematics, University of California, San Diego, CA, 1988. - -%\bibitem{HBMG} -%R.~E. Bank, T.~F. Dupont, and H.~Yserentant, {\em The hierarchical basis -% multigrid method}, Numer. Math., 52 (1988), pp.~427--458. - -\bibitem{BANKSMITH} -R.~E. Bank and R.~K. Smith, {\em General sparse elimination requires no - permanent integer storage}, SIAM J. Sci. Stat. Comput., 8 (1987), - pp.~574--584. - -\bibitem{EISENSTAT} -S.~C. Eisenstat, M.~C. Gursky, M.~Schultz, and A.~Sherman, {\em - Algorithms and data structures for sparse symmetric gaussian elimination}, - SIAM J. Sci. Stat. Comput., 2 (1982), pp.~225--237. - -\bibitem{GEORGELIU} -A.~George and J.~Liu, {\em Computer Solution of Large Sparse Positive - Definite Systems}, Prentice Hall, Englewood Cliffs, NJ, 1981. - -\bibitem{LAW} -K.~H. Law and S.~J. Fenves, {\em A node addition model for symbolic - factorization}, ACM TOMS, 12 (1986), pp.~37--50. - -\bibitem{LIU} -J.~W.~H. Liu, {\em A compact row storage scheme for cholesky factors - using elimination trees}, ACM TOMS, 12 (1986), pp.~127--148. - -\bibitem{LIU2} -\sameauthor , {\em The role of - elimination trees in sparse factorization}, Tech. Report CS-87-12,Department - of Computer Science, York University, Ontario, Canada, 1987. - -\bibitem{ROSE72} -D.~J. Rose, {\em A graph theoretic study of the numeric solution of - sparse positive definite systems}, in Graph Theory and Computing, Academic Press, New -York, 1972. - -\bibitem{ROSE76} -D.~J. Rose, R.~E. Tarjan, and G.~S. Lueker, {\em Algorithmic aspects of - vertex elimination on graphs}, SIAM J. Comput., 5 (1976), pp.~226--283. - -\bibitem{ROSEWHITTEN} -D.~J. Rose and G.~F. Whitten, {\em A recursive analysis of disection - strategies}, in Sparse Matrix Computations, Academic Press, New York, 1976. - -\bibitem{SCHREIBER} -R.~Schrieber, {\em A new implementation of sparse gaussian elimination}, - ACM TOMS, 8 (1982), pp.~256--276. - -\end{thebibliography} -\end{document} - -% End of ltexpprt.tex -% - - - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% ltexpprt.sty %%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% -% This is ltexpprt.sty, a file of macros and definitions for creating a -% chapter for publication in the ACM/SIAM Preprint series using LaTeX2E. -% It is designed to produce double-column output. -% This file may be freely distributed but may not be altered in any way. -% Any comments or questions regarding these macros should be directed to: - -% Corey Gray -% SIAM -% 3600 University City Science Center -% Philadelphia, PA 19104-2688 -% USA -% Telephone: (215) 382-9800 -% Fax: (215) 386-7999 -% e-mail: gray@siam.org - - -% Report the version. -\message{*** ACM/SIAM LaTeX2E Preprint Series macro package, version 1.0, -September 5, 1996 ***} - - -\pretolerance=800 -\tolerance=10000 -\sloppy - -%\voffset=-.5in -%\hoffset=-.5in -\vsize=55pc -\hsize=41pc -\baselineskip=14pt -\footskip=18pt -\topmargin 24pt -\headheight 12pt -\headsep 17pt -\textheight 52.5pc \advance\textheight by \topskip -\textwidth 41pc -\parskip 0pt -\parindent 18pt - -\font\tensmc=cmcsc10 -\def\smc{\tensmc} - -%% footnotes to be set 8/10 -\def\footnotesize{\@setsize\footnotesize{10pt}\viiipt\@viiipt - % \indent - \abovedisplayskip \z@ - \belowdisplayskip\z@ - \abovedisplayshortskip\abovedisplayskip - \belowdisplayshortskip\belowdisplayshortskip - \def\@listi{\leftmargin\leftmargini \topsep 3pt plus 1pt minus 1pt - \parsep 2pt plus 1pt minus 1pt - \itemsep \parsep}} - -\let\referencesize\footnotesize - -\footnotesep 0pt - -\skip\footins 12pt plus 12pt - -\def\footnoterule{\kern3\p@ \hrule width 3em} % the \hrule is .4pt high - -\def\ps@plain{\let\@mkboth\@gobbletwo - \def\@oddfoot{{\hfil\small\thepage\hfil}}% - \def\@oddhead{} - \def\@evenhead{}\def\@evenfoot{}} - - - - - -\def\ps@headings{\let\@mkboth\markboth - \def\@oddfoot{}\def\@evenfoot{}% - \def\@evenhead{{\rm\thepage}\hfil{\small\leftmark}}% - \def\@oddhead{{\noindent\small\rightmark}\hfil{\rm\thepage}}% - - - -\def\ps@myheadings{\let\@mkboth\@gobbletwo - \def\@oddfoot{}\def\@evenfoot{}% - \def\@oddhead{\rlap{\normalsize\rm\rightmark}\hfil{small\thepage}}% - \def\@evenhead%{\hfil{\small\@chapapp}\ - {\small\thepage}\hfil\llap{\normalsize\rm\leftmark}}% - \def\chaptermark##1{}% - \def\sectionmark##1{}\def\subsectionmark##1{}} - - -\def\theequation{\arabic{section}.\arabic{equation}} - - -\def\section{\@startsection{section}{1}{0pt}{-12pt}{3pt}{\hyphenpenalty=\@M -\exhyphenpenalty=\@M\normalsize\bf}} -\def\subsection{\@startsection{subsection}{2}{0pt}{-12pt}{0pt}{\normalsize\bf} -} -\def\subsubsection{\@startsection - {subsubsection}{3}{0pt}{-12pt}{0pt}{\normalsize\bf}} -\def\paragraph{\@startsection - {paragraph}{4}{\parindent}{0pt}{0pt}{\normalsize\bf}} -\def\subparagraph{\@startsection - {subparagraph}{4}{\parindent}{0pt}{0pt}{\normalsize\bf}} - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% % -% THEOREMS, PROOFS, ALGORITHMS % -% % -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -%%% defined proof environment by theorem model (took out counter) - -\def\newproof#1{\@nprf{#1}} - -\def\@nprf#1#2{\@xnprf{#1}{#2}} - -\def\@xnprf#1#2{\expandafter\@ifdefinable\csname #1\endcsname -\global\@namedef{#1}{\@prf{#1}{#2}}\global\@namedef{end#1}{\@endproof}} - -\def\@prf#1#2{\@xprf{#1}{#2}} - -\def\@xprf#1#2{\@beginproof{#2}{\csname the#1\endcsname}\ignorespaces} - - - -%%% defined algorithm environment by theorem model - -\def\newalgorithm#1{\@ifnextchar[{\@oalg{#1}}{\@nalg{#1}}} - -\def\@nalg#1#2{% -\@ifnextchar[{\@xnalg{#1}{#2}}{\@ynalg{#1}{#2}}} - -\def\@xnalg#1#2[#3]{\expandafter\@ifdefinable\csname #1\endcsname -{\@definecounter{#1}\@addtoreset{#1}{#3}% -\expandafter\xdef\csname the#1\endcsname{\expandafter\noexpand - \csname the#3\endcsname \@thmcountersep \@thmcounter{#1}}% -\global\@namedef{#1}{\@alg{#1}{#2}}\global\@namedef{end#1}{\@endalgorithm}}} - -\def\@ynalg#1#2{\expandafter\@ifdefinable\csname #1\endcsname -{\@definecounter{#1}% -\expandafter\xdef\csname the#1\endcsname{\@thmcounter{#1}}% -\global\@namedef{#1}{\@alg{#1}{#2}}\global\@namedef{end#1}{\@endalgorithm}}} - -\def\@oalg#1[#2]#3{\expandafter\@ifdefinable\csname #1\endcsname - {\global\@namedef{the#1}{\@nameuse{the#2}}% -\global\@namedef{#1}{\@alg{#2}{#3}}% -\global\@namedef{end#1}{\@endalgorithm}}} - -\def\@alg#1#2{\refstepcounter - {#1}\@ifnextchar[{\@yalg{#1}{#2}}{\@xalg{#1}{#2}}} - -\def\@xalg#1#2{\@beginalgorithm{#2}{\csname the#1\endcsname}\ignorespaces} -\def\@yalg#1#2[#3]{\@opargbeginalgorithm{#2}{\csname - the#1\endcsname}{#3}\ignorespaces} - - - - -\def\@beginproof#1{\rm \trivlist \item[\hskip \labelsep{\it #1.\/}]} -\def\@endproof{\outerparskip 0pt\endtrivlist} - -\def\@begintheorem#1#2{\it \trivlist \item[\hskip \labelsep{\sc #1\ #2.}]} -\def\@opargbegintheorem#1#2#3{\it \trivlist - \item[\hskip \labelsep{\sc #1\ #2.\ (#3)}]} -\def\@endtheorem{\outerparskip 0pt\endtrivlist} - -%\def\@begindefinition#1#2{\rm \trivlist \item[\hskip \labelsep{\sc #1\ #2.}]} -%\def\@opargbegindefinition#1#2#3{\rm \trivlist -% \item[\hskip \labelsep{\sc #1\ #2.\ (#3)}]} -%\def\@enddefinition{\outerparskip 0pt\endtrivlist} - - -\def\@beginalgorithm#1#2{\rm \trivlist \item[\hskip \labelsep{\sc #1\ #2.}]} -\def\@opargbeginalgorithm#1#2#3{\rm \trivlist - \item[\hskip \labelsep{\sc #1\ #2.\ (#3)}]} -\def\@endalgorithm{\outerparskip 6pt\endtrivlist} - - -\newskip\outerparskip - -%\def\trivlist{\parsep\outerparskip -% \@trivlist \labelwidth\z@ \leftmargin\z@ -% \itemindent\parindent \def\makelabel##1{##1}} -% -%\def\@trivlist{\topsep=0pt\@topsepadd\topsep -% \if@noskipsec \leavevmode \fi -% \ifvmode \advance\@topsepadd\partopsep \else \unskip\par\fi -% \if@inlabel \@noparitemtrue \@noparlisttrue -% \else \@noparlistfalse \@topsep\@topsepadd \fi -% \advance\@topsep \parskip -% \leftskip\z@\rightskip\@rightskip \parfillskip\@flushglue -% \@setpar{\if@newlist\else{\@@par}\fi}% -% \global\@newlisttrue \@outerparskip\parskip} -% -% -%\def\endtrivlist{\if@newlist\@noitemerr\fi -% \if@inlabel\indent\fi -% \ifhmode\unskip \par\fi -% \if@noparlist \else -% \ifdim\lastskip >\z@ \@tempskipa\lastskip \vskip -\lastskip -% \advance\@tempskipa\parskip \advance\@tempskipa -\@outerparskip -% \vskip\@tempskipa -% \fi\@endparenv\fi -% \vskip\outerparskip} - - - - \newproof{@proof}{Proof} - \newenvironment{proof}{\begin{@proof}}{\end{@proof}} - - \newtheorem{@theorem}{Theorem}[section] - \newenvironment{theorem}{\begin{@theorem}}{\end{@theorem}} - - \newalgorithm{@algorithm}{Algorithm}[section] - \newenvironment{algorithm}{\begin{@algorithm}}{\end{@algorithm}} - - - -\newtheorem{lemma}{Lemma}[section] -\newtheorem{fact}{Fact}[section] -\newtheorem{corollary}{Corollary}[section] -\newtheorem{axiom}{Axiom}[section] -\newtheorem{cond}{Condition}[section] -\newtheorem{property}{Property}[section] -\newtheorem{proposition}{Proposition}[section] - -\newtheorem{Conjecture}{Conjecture}[section] -%\newtheorem{Corollary}[Theorem]{Corollary} -\newtheorem{Definition}{Definition}[section] -\newtheorem{Lemma}{Lemma}[section] -\newtheorem{Remark}{Remark}[section] - -\newproof{Example}{Example} -\newproof{Method}{Method} -\newproof{Exercise}{Exercise} - - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% %% -%% BIBLIOGRAPHY %% -%% %% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - - -\def\thebibliography#1{% -%\cleardoublepage -\parindent 0em -\vspace{6pt} -\begin{flushleft}\normalsize\bf References\end{flushleft} -\addvspace{3pt}\nopagebreak\list - %% default is no labels, for those not using \cite or BibTeX -% {[\arabic{enumi}]} {\settowidth\labelwidth{[#1]} -{[\arabic{enumi}]}{\settowidth\labelwidth{mm} -\leftmargin\labelwidth - \advance\leftmargin\labelsep - \usecounter{enumi}\@bibsetup} -\def\newblock{\hskip .11em plus .33em minus -.07em} - \sloppy\clubpenalty4000\widowpenalty4000 - \sfcode`\.=1000\relax} - -%% setup 8/10 type -\def\@bibsetup{\itemindent=0pt \itemsep=0pt \parsep=0pt -\small} - -\def\sameauthor{\leavevmode\vrule height 2pt depth -1.6pt width 23pt} - -% -% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% CUT HERE %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% -% -% - diff --git a/Master/texmf-dist/source/latex/siam/sodaptex.all b/Master/texmf-dist/source/latex/siam/sodaptex.all deleted file mode 100644 index e4c99f08c2b..00000000000 --- a/Master/texmf-dist/source/latex/siam/sodaptex.all +++ /dev/null @@ -1,722 +0,0 @@ -%% This is sodaptex.all. This file is to be used for creating a paper -%% in the ACM/SIAM Preprint series with Plain TeX. It consists of the following -%% two files: -%% -%% ptexpprt.tex ---- an example and documentation file -%% ptexpprt.sty ---- the macro file -%% -%% To use, cut this file apart at the appropriate places. You can run the -%% example file with the macros to get sample output. -%% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%% CUT HERE %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% -% -%%%%%%%%%%%%%%%%%%%%%%%%%% ptexpprt.tex %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% -% This is ptexpprt.tex, an example file for use with the ACM/SIAM Plain TeX -% Preprint Series macros. It is designed to produce double-column output. -% Comments are placed at the beginning and throughout this file. Please -% take the time to read them as they document how to use these macros. -% This file can be composed and printed out for use as sample output. - -% Any comments or questions regarding these macros should be directed to: -% -% Corey Gray -% SIAM -% 3600 University City Science Center -% Philadelphia, PA 19104-2688 -% USA -% Telephone: (215) 382-9800 -% Fax: (215) 386-7999 -% e-mail: gray@siam.org - -% This file is to be used as an example for style only. It should not be read -% for content. - -%%%%%%%%%%%%%%% PLEASE NOTE THE FOLLOWING STYLE RESTRICTIONS %%%%%%%%%%%%%%% - -%% 1. You must use the numbered reference style([1],[2]), listing the -%% references at the end of the chapter either by order of citation -%% or alphabetically. -%% -%% 2. Unless otherwise stated by your editor, do your chapter as if it -%% is Chapter 1. -%% If you know which number your chapter is, you must do the following: -%% -%% Go into the style file (ptexfrnt.sty) and search for the -%% \def\chapter#1 definition. At the end of this definition -%% there is a command \headcount=1. Change the 1 to -%% the appropriate number. This change will cause the headings -%% in your chapter to match the chapter number. -%% -%% 3. This macro is set up for two levels of headings. The macro will -%% automatically number the headings for you. -%% -%% 4. The running heads are defined in the output routine. It will be -%% necessary for you to alter the information currently included. -%% To do this, go into the style file and search for OUTPUT. Once there, -%% scroll through the file until you see the command \def\rhead. Replace -%% CHAPTER TITLE with the title (or shortened title) of your paper. -%% Replace AUTHORS NAMES with the appropriate names. -%% Neither running head may be longer than 50 characters. -%% -%% 5. Theorems, Lemmas, Definitions, etc. are to be triple numbered, -%% indicating the chapter, section, and the occurence of that element -%% within that section. (For example, the first theorem in the second -%% section of chapter three would be numbered 3.2.1. This numbering must -%% be done manually. -%% -%% 6. Figures and equations must be manually double-numbered, indicating -%% chapter and occurence. Use \leqno for equation numbering. See the -%% example of \caption for figure numbering. -%% Note. Although not shown, tables must also be double-numbered. The -%% command \caption can also be used for table captions. -%% -%% 7. At the first occurence of each new element there is a description -%% of how to use the coding. -%% -%%%%%%% PLEASE NOTE THE FOLLOWING POTENTIAL PROBLEMS: -% -%% 1. A bug exists that prevents a page number from printing on the first -%% page of the paper. Please ignore this problem. It will be handled -%% after you submit your paper. -%% -%% 2. The use of \topinsert and \midinsert to allow space for figures can -%% result in unusual page breaks, or unusual looking pages in general. -%% If you encounter such a situation, contact the SIAM office at the -%% address listed above for instructions. -%% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -\input ptexpprt.sty -\voffset=.25in -\titlepage - -% It will be necessary to hard code the chapter title and chapter authors. -% You must decide where to break the lines. For the authors, please follow -% the following conventions: -% 1. If 2 authors are on a line, use \hskip4pc between them. If 3 authors, -% use \hskip2pc. Do not put more than 3 authors on the same line. -% 2. Use the following notation: asterisk, dagger, double-dagger, section -% symbol, paragraph symbol, double asterisk. If more are needed, contact -% the SIAM office. - -\centerline{\chapterfont Chapter 1} -\vskip2pt -\centerline{\titlefont SIAM/ACM Preprint Series Macros for -Plain TeX\footnote*{Supported by GSF grants ABC123, DEF456, and GHI 789.}} -\vskip15pt -\centerline{\authorfont J. Corey Gray\footnote\dag{Society for Industrial and -Applied Mathematics.}\hskip2pc Tricia Manning\footnote\ddag{Society for -Industrial and Applied Mathematics.}\hskip2pc Vickie Kearn\footnote\S{Society -for Industrial and Applied Mathematics.}} -\vskip2pc - -\begindoublecolumns - -% Use \headone for the first level headings. The macro will automatically -% number the headings. - -\headone{Problem Specification} -In this paper, we consider the solution of the $N \times N$ linear -system -$$A x = b\leqno(1.1)$$ -where $A$ is large, sparse, symmetric, and positive definite. We consider -the direct solution of by means of general sparse Gaussian -elimination. In such a procedure, we find a permutation matrix $P$, and -compute the decomposition -$$ -P A P^{t} = L D L^{t} -$$ -where $L$ is unit lower triangular and $D$ is diagonal. - -\headone{Design Considerations} -Several good ordering algorithms (nested dissection and minimum degree) -are available for computing $P$ [1], [2]. -Since our interest here does not -focus directly on the ordering, we assume for convenience that $P=I$, -or that $A$ has been preordered to reflect an appropriate choice of $P$. - -% Use \headtwo for second level headings. They will be numbered automatically. - -\headtwo{Robustness}In \S 1.2, we review the bordering algorithm, and introduce -the sorting and intersection problems that arise in the -sparse formulation of the algorithm. - -\headtwo{Versatility} In \S 1.3., we analyze the complexity of the old and new -approaches to the intersection problem for the special case of -an $n \times n$ grid ordered by nested dissection. The special -structure of this problem allows us to make exact estimates of -the complexity. To our knowledge, the m-tree previously has not been applied in -this -fashion to the numerical factorization, but it has been used, -directly or indirectly, in several optimal order algorithms for -computing the fill-in during the symbolic factorization phase -[4] - [10], [5], [6]. -This is accomplished by exploiting the m-tree, -a particular spanning tree for the graph of the filled-in matrix. -Our purpose here is to examine the nonnumerical complexity of the -sparse elimination algorithm given in [3]. -As was shown there, a general sparse elimination scheme based on the -bordering algorithm requires less storage for pointers and -row/column indices than more traditional implementations of general -sparse elimination. This is accomplished by exploiting the m-tree, -a particular spanning tree for the graph of the filled-in matrix. - - -% Use \thm and \endthm for theorems. They must be numbered manually. -% Lemmas (\lem \endlem), corollaries (\cor \endcor), and -% propositions (\prop \endprop) are coded the same as theorems and must -% also be numbered manually. - -\thm{Theorem 2.1.} The method was extended to three -dimensions. For the standard multigrid -coarsening -(in which, for a given grid, the next coarser grid has $1/8$ -as many points), anisotropic problems require plane -relaxation to -obtain a good smoothing factor.\endthm - -Several good ordering algorithms (nested dissection and minimum degree) -are available for computing $P$ [1], [2]. -Since our interest here does not -focus directly on the ordering, we assume for convenience that $P=I$, -or that $A$ has been preordered to reflect an appropriate choice of $P$. -Several good ordering algorithms (nested dissection and minimum degree) -are available for computing $P$ [1], [2]. -Since our interest here does not -focus directly on the ordering, we assume for convenience that $P=I$, -or that $A$ has been preordered to reflect an appropriate choice of $P$. - -% Use \prf to begin a proof. - -\prf{Proof} In this paper we consider two methods. The first method -is -basically the method considered with two differences: -first, we perform plane relaxation by a two-dimensional -multigrid method, and second, we use a slightly different -choice of -interpolation operator, which improves performance -for nearly singular problems. In the second method coarsening -is done by successively coarsening each. - -% Use \dfn to begin definitions. - -\dfn{Definition 1.2.1.}We describe the two methods in \S\ 1.2. This is a -definition in the plain tex macro. - -This is accomplished by exploiting the m-tree, -a particular spanning tree for the graph of the filled-in matrix. -Our purpose here is to examine the nonnumerical complexity of the -sparse elimination algorithm given in [3]. -As was shown there, a general sparse elimination scheme based on the -bordering algorithm requires less storage for pointers and -row/column indices than more traditional implementations of general -sparse elimination. This is accomplished by exploiting the m-tree, -a particular spanning tree for the graph of the filled-in matrix. -Our purpose here is to examine the nonnumerical complexity of the -sparse elimination algorithm given in [3]. -As was shown there, a general sparse elimination scheme based on the -bordering algorithm requires less storage for pointers and -row/column indices than more traditional implementations of general -sparse elimination. This is accomplished by exploiting the m-tree, -a particular spanning tree for the graph of the filled-in matrix. -Since our interest here does not -focus directly on the ordering, we assume for convenience that $P=I$, -or that $A$ has been preordered to reflect an appropriate choice of $P$. - - -To our knowledge, the m-tree previously has not been applied in this -fashion to the numerical factorization, but it has been used, -directly or indirectly, in several optimal order algorithms for -computing the fill-in during the symbolic factorization phase -[4] - [10], [5], [6]. In \S 1.3., we analyze the complexity of the old and new -approaches to the intersection problem for the special case of -an $n \times n$ grid ordered by nested dissection. The special -structure of this problem allows us to make exact estimates of -the complexity. To our knowledge, the m-tree previously has not been applied in -this -fashion to the numerical factorization, but it has been used, -directly or indirectly, in several optimal order algorithms for -computing the fill-in during the symbolic factorization phase -[4] - [10], [5], [6]. -Several good ordering algorithms (nested dissection and minimum degree) -are available for computing $P$ [1], [2]. -Since our interest here does not -focus directly on the ordering, we assume for convenience that $P=I$, -or that $A$ has been preordered to reflect an appropriate choice of $P$. -For the old approach, we show that the -complexity of the intersection problem is $O(n^{3})$, the same -as the complexity of the numerical computations. For the -new approach, the complexity of the second part is reduced to -$O(n^{2} (\log n)^{2})$. - -% Use \midinsert along with \caption to allow space for -% figures. See note above in problem section. -%\midinsert\vskip15.5pc\caption{Fig. 1.1. {\nineit This is figure 1.}} -% \endcaption\endinsert - -In this paper, we consider the solution of the $N \times N$ linear -system -where $A$ is large, sparse, symmetric, and positive definite. We consider -the direct solution of by means of general sparse Gaussian -elimination. In such a procedure, we find a permutation matrix $P$, and -compute the decomposition -where $L$ is unit lower triangular and $D$ is diagonal. - -\headone{Design Considerations} -Several good ordering algorithms (nested dissection and minimum degree) -are available for computing $P$ [1], [2]. -Since our interest here does not -focus directly on the ordering, we assume for convenience that $P=I$, -or that $A$ has been preordered to reflect an appropriate choice of $P$. - -Several good ordering algorithms (nested dissection and minimum degree) -are available for computing $P$ [1], [2]. -Since our interest here does not -focus directly on the ordering, we assume for convenience that $P=I$, -or that $A$ has been preordered to reflect an appropriate choice of $P$. -Several good ordering algorithms (nested dissection and minimum degree) -are available for computing $P$ [1], [2]. -Since our interest here does not -focus directly on the ordering, we assume for convenience that $P=I$, -or that $A$ has been preordered to reflect an appropriate choice of $P$. -Our purpose here is to examine the nonnumerical complexity of the -sparse elimination algorithm given in [3]. -As was shown there, a general sparse elimination scheme based on the -bordering algorithm requires less storage for pointers and -row/column indices than more traditional implementations of general -sparse elimination. This is accomplished by exploiting the m-tree, -a particular spanning tree for the graph of the filled-in matrix. -Since our interest here does not -focus directly on the ordering, we assume for convenience that $P=I$, -or that $A$ has been preordered to reflect an appropriate choice of $P$. - -% Use \lem and \endlem to begin and end lemmas. - -\lem{Lemma 2.1.}We discuss first the choice for $I_{k-1}^k$ -which is a generalization. We assume that $G^{k-1}$ is -obtained -from $G^k$ -by standard coarsening; that is, if $G^k$ is a tensor product -grid $G_{x}^k \times G_{y}^k \times G_{z}^k$, -$G^{k-1}=G_{x}^{k-1} \times G_{y}^{k-1} \times G_{z}^{k-1}$, -where $G_{x}^{k-1}$ is obtained by deleting every other grid -point of $G_x^k$ and similarly for $G_{y}^k$ and $G_{z}^k$. -\endlem - -To our knowledge, the m-tree previously has not been applied in this -fashion to the numerical factorization, but it has been used, -directly or indirectly, in several optimal order algorithms for -computing the fill-in during the symbolic factorization phase -[4] - [10], [5], [6]. In \S 1.3., we analyze the complexity of the old and new -approaches to the intersection problem for the special case of -an $n \times n$ grid ordered by nested dissection. The special -structure of this problem allows us to make exact estimates of -the complexity. To our knowledge, the m-tree previously has not been applied in -this -fashion to the numerical factorization, but it has been used, -directly or indirectly, in several optimal order algorithms for -computing the fill-in during the symbolic factorization phase -[4] - [10], [5], [6]. - -% Use \headtwo for second level headings. They will be numbered automatically. - -\headone{Problem Solving}In \S 1.2, we review the bordering algorithm, and -introduce -the sorting and intersection problems that arise in the -sparse formulation of the algorithm. - -\headtwo{Versatility} In \S 1.3., we analyze the complexity of the old and new -approaches to the intersection problem for the special case of -an $n \times n$ grid ordered by nested dissection. The special -structure of this problem allows us to make exact estimates of -the complexity. To our knowledge, the m-tree previously has not been applied in -this -fashion to the numerical factorization, but it has been used, -directly or indirectly, in several optimal order algorithms for -computing the fill-in during the symbolic factorization phase -[4] - [10], [5], [6]. - - -\headtwo{Complexity}For the old approach, we show that the -complexity of the intersection problem is $O(n^{3})$, the same -as the complexity of the numerical computations. For the -new approach, the complexity of the second part is reduced to -$O(n^{2} (\log n)^{2})$. - -To our knowledge, the m-tree previously has not been applied in this -fashion to the numerical factorization, but it has been used, -directly or indirectly, in several optimal order algorithms for -computing the fill-in during the symbolic factorization phase -[4] - [10], [5], [6]. In \S 1.3., we analyze the complexity of the old and new -approaches to the intersection problem for the special case of -an $n \times n$ grid ordered by nested dissection. The special -structure of this problem allows us to make exact estimates of -the complexity. To our knowledge, the m-tree previously has not been applied in -this -fashion to the numerical factorization, but it has been used, -directly or indirectly, in several optimal order algorithms for -computing the fill-in during the symbolic factorization phase -[4] - [10], [5], [6]. - -% The command \Refs sets the word Reference as a heading and allows the proper -% amount of space before the start of the references. Each reference must -% begin with \ref\\. The article or title of the reference should be in -% italic. Use the \it command within brackets. End each reference with -% \endref and allow two returns between references. Use the command -% \sameauthor (see reference 8) when the same author or group of authors -% is listed consecutively. - -\Refs - -\ref 1\\R.~E. Bank, {\it PLTMG users' guide, edition 5.0}, tech. report, - Department of Mathematics, University of California, San Diego, CA, -1988.\endref - -\ref 2\\R.~E. Bank, T.~F. Dupont, and H.~Yserentant, {\it The hierarchical basis - multigrid method}, Numer. Math., 52 (1988), pp.~427--458.\endref - -\ref 3\\R.~E. Bank and R.~K. Smith, {\it General sparse elimination requires no - permanent integer storage}, SIAM J. Sci. Stat. Comput., 8 (1987), - pp.~574--584.\endref - -\ref 4\\S.~C. Eisenstat, M.~C. Gursky, M.~Schultz, and A.~Sherman, {\it - Algorithms and data structures for sparse symmetric gaussian elimination}, - SIAM J. Sci. Stat. Comput., 2 (1982), pp.~225--237.\endref - -\ref 5\\A.~George and J.~Liu, {\it Computer Solution of Large Positive - Definite Systems}, Prentice Hall, Englewood Cliffs, NJ, 1981.\endref - -\ref 6\\K.~H. Law and S.~J. Fenves, {\it A node addition model for symbolic - factorization}, ACM TOMS, 12 (1986), pp.~37--50.\endref - -\ref 7\\J.~W.~H. Liu, {\it A compact row storage scheme for factors - using elimination trees}, ACM TOMS, 12 (1986), pp.~127--148.\endref - -\ref 8\\\sameauthor , {\it The role of - elimination trees in sparse factorization}, Tech. Report CS-87-12,Department - of Computer Science, York University, Ontario, Canada, 1987.\endref - -\ref 9\\D.~J. Rose, {\it A graph theoretic study of the numeric solution of - sparse positive definite systems}, in Graph Theory and Computing, - Academic Press, New York, 1972.\endref - -\ref 10\\D.~J. Rose, R.~E. Tarjan, and G.~S. Lueker, {\it Algorithmic aspects of - vertex elimination on graphs}, SIAM J. Comput., 5 (1976), pp.~226--283.\endref -\enddoublecolumns - -\bye -%% -%% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%% CUT HERE %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% -% -%%%%%%%%%%%%%%%%%%%%%%%%%% ptexpprt.sty %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% -% This is a file of macros and definitions for creating a chapter -% for publication in the ACM/SIAM Preprint Series using Plain TeX. -% This file may be freely distributed but may not be altered in any way. -% Any comments or questions regarding these macros should be directed to: - -% Corey Gray -% SIAM -% 3600 University City Science Center -% Philadelphia, PA 19104-2688 -% USA -% Telephone: (215) 382-9800 -% Fax: (215) 386-7999 -% e-mail: gray@siam.org -% - -% Report the version. -\message{*** ACM/SIAM Plain TeX Preprint Series macro package, version 1.0, -September 24, 1990.***} - -% Make the @ sign a letter for internal control sequences. -\catcode`\@=11 -% -% -% - - - -%%% DIMENSIONS %%% - -\newdimen\pagewidth -\hsize=41pc -\pagewidth=\hsize -\newdimen\pageheight -\vsize=50pc -\pageheight=\vsize -\newdimen\ruleht -\ruleht=.5pt -\maxdepth=2.2pt - -\parindent=18truept -\def\firstpar{\parindent=0pt\global\everypar{\parindent=18truept}} -\parskip=0pt plus 1pt - - -%%% FONTS %%% - -\font\tenrm=cmr10 -\font\tenbf=cmbx10 -\font\tenit=cmti10 -\font\tensmc=cmcsc10 -\def\tenpoint{% - \def\rm{\tenrm}\def\bf{\tenbf}% - \def\it{\tenit}\def\smc{\tensmc} - \textfont0=\tenrm \scriptfont0=\sevenrm - \textfont1=\teni \scriptfont1=\seveni - \textfont2=\tensy \scriptfont2=\sevensy - \textfont3=\tenex \scriptfont3=\tenex -\baselineskip=12pt\rm}% - -\font\ninerm=cmr9 -\font\ninebf=cmbx9 -\font\nineit=cmti9 -\def\ninepoint{% - \def\rm{\ninerm}\def\bf{\ninebf}% - \def\it{\nineit}\baselineskip=11pt\rm}% - -\font\eightrm=cmr8 -\font\eightbf=cmbx8 -\font\eightit=cmti8 -\font\eighti=cmmi8 -\font\eightsy=cmsy8 -\def\eightpoint{% - \def\rm{\eightrm}\def\bf{\eightbf}% - \def\it{\eightit}\def\smc{\eightrm}\baselineskip=10pt\rm% - \textfont0=\eightrm \scriptfont0=\sixrm - \textfont1=\eighti \scriptfont1=\sixi - \textfont2=\eightsy \scriptfont2=\sixsy - \textfont3=\tenex \scriptfont3=\tenex -} - -\font\sixrm=cmr6 -\font\sixbf=cmbx6 -\font\sixi=cmmi6 -\font\sixsmc=cmr5 -\font\sixsy=cmsy6 -\def\sixpoint{% - \def\rm{\sixrm}\def\bf{\sixbf}% - \def\smc{\sixsmc}\baselineskip=8pt\rm}% - -\fontdimen13\tensy=2.6pt -\fontdimen14\tensy=2.6pt -\fontdimen15\tensy=2.6pt -\fontdimen16\tensy=1.2pt -\fontdimen17\tensy=1.2pt -\fontdimen18\tensy=1.2pt - -\font\eightrm=cmr8 -\font\ninerm=cmr9 -\font\twelverm=cmr10 scaled\magstep1 -\font\twelvebf=cmbx10 scaled\magstep 1 -\font\sixteenrm=cmr10 scaled\magstep2 -\def\titlefont{\sixteenrm} -\def\chapterfont{\twelvebf} -\def\authorfont{\twelverm} -\def\rheadfont{\tenrm} -\def\smc{\tensmc} - - - - -%%% COUNTERS FOR HEADINGS %%% - -\newcount\headcount -\headcount=1 -\newcount\seccount -\seccount=1 -\newcount\subseccount -\subseccount=1 -\def\reset{\global\seccount=1} -\global\headcount=0 - -%%% HEADINGS %%% - -\def\headone#1{\global\advance\headcount by 1 -\vskip12truept\parindent=0pt{\tenpoint\bf\the\headcount -\hskip11truept #1.}\par\nobreak\firstpar\global\advance\headcount by 0 - %\global\advance\seccount by 1 -\reset\vskip2truept} - -\def\headtwo#1{%\advance\seccount by -1% - \vskip12truept\parindent=0pt{\tenpoint\bf\the\headcount.% - \the\seccount\hskip11truept #1.}\enspace\ignorespaces\firstpar - \global\advance\headcount by 0\global\advance\seccount by 1} -% \global\advance\subseccount by 1} - - -%%% THEOREMS, PROOFS, DEFINITIONS, etc. %%% - -\def\thm#1{{\smc -#1\enspace} -\begingroup\it\ignorespaces\firstpar} - -\let\lem=\thm -\let\cor=\thm -\let\prop=\thm - -\def\endthm{\endgroup} -\let\endlem=\endthm -\let\endcor=\endthm -\let\endprop=\endthm - -\def\prf#1{{\it #1.}\rm\enspace\ignorespaces} -\let\rem=\prf -\let\case=\prf - - -\def\dfn#1{{\smc -#1\enspace} -\rm\ignorespaces} - - - -%%% FIGURES AND CAPTIONS %%% - -\def\caption#1\endcaption{\vskip18pt\ninerm\centerline{#1}\vskip18pt\tenrm} - -\newinsert\topins \newif\ifp@ge \newif\if@mid -\def\topinsert{\@midfalse\p@gefalse\@ins} -\def\midinsert{\@midtrue\@ins} -\def\pageinsert{\@midfalse\p@getrue\@ins} -\skip\topins=0pt %no space added when a topinsert is present -\count\topins=1000 %magnification factor (1 to 1) -\dimen\topins=\maxdimen -\def\@ins{\par\begingroup\setbox0=\vbox\bgroup} -\def\endinsert{\egroup - \if@mid \dimen@=\ht0 \advance\dimen@ by\dp0 - \advance\dimen@ by12\p@ \advance\dimen@ by\pagetotal - \ifdim\dimen@>\pagegoal \@midfalse\p@gefalse\fi\fi - \if@mid \bigskip \box0 \bigbreak - \else\insert\topins{\penalty100 - \splittopskip=0pt \splitmaxdepth=\maxdimen \floatingpenalty=0 - \ifp@ge \dimen@=\dp0 - \vbox to\vsize{\unvbox0 \kern-\dimen@} - \else \box0 \nobreak\bigskip\fi}\fi\endgroup} - - -%%% REFERENCES %%% - -\newdimen\refindent@ -\newdimen\refhangindent@ -\newbox\refbox@ -\setbox\refbox@=\hbox{\ninepoint\rm\baselineskip=11pt [00]}% Default 2 digits -\refindent@=\wd\refbox@ - -\def\resetrefindent#1{% - \setbox\refbox@=\hbox{\ninepoint\rm\baselineskip=11pt [#1]}% - \refindent@=\wd\refbox@} - -\def\Refs{% - \unskip\vskip1pc - \leftline{\noindent\tenpoint\bf References}% - \penalty10000 - \vskip4pt - \penalty10000 - \refhangindent@=\refindent@ - \global\advance\refhangindent@ by .5em - \global\everypar{\hangindent\refhangindent@}% - \parindent=0pt\ninepoint\rm} - -\def\sameauthor{\leavevmode\vbox to 1ex{\vskip 0pt plus 100pt - \hbox to 2em{\leaders\hrule\hfil}\vskip 0pt plus 300pt}} - -\def\ref#1\\#2\endref{\leavevmode\hbox to \refindent@{\hfil[#1]}\enspace #2\par} - - -%%% OUTPUT %%% - -\newinsert\margin -\dimen\margin=\maxdimen -\count\margin=0 \skip\margin=0pt - - -\def\footnote#1{\edef\@sf{\spacefactor\the\spacefactor}#1\@sf - \insert\footins\bgroup\eightpoint\hsize=30pc - \interlinepenalty100 \let\par=\endgraf - \leftskip=0pt \rightskip=0pt - \splittopskip=10pt plus 1pt minus 1pt \floatingpenalty=20000 -\smallskip -\item{#1}\bgroup\strut\aftergroup\@foot\let\next} -\skip\footins=6pt plus 2pt minus 4pt -\dimen\footins=30pc - -\newif\iftitle - - -\def\titlepage{\global\titletrue\footline={\hss\ninepoint\rm\folio\hss}} -\def\rhead{\ifodd\pageno CHAPTER TITLE - \else AUTHORS NAMES\fi} - -\def\makefootline{\ifnum\pageno>1\global\footline={\hfill}\fi - \baselineskip24\p@\vskip12\p@\fullline{\the\footline}} -\def\leftheadline{\hbox to \pagewidth{ - \vbox to 10pt{} - {\kern-8pt\tenrm\folio\hfill\ninerm\rhead}}} -\def\rightheadline{\hbox to \pagewidth{ - \vbox to 10pt{} - \kern-8pt\ninerm\rhead\hfil - {\kern-1pc\tenrm\folio}}} - -\def\onepageout#1{\shipout\vbox{ -\offinterlineskip - \vbox to 2.25pc{% - \iftitle \global\titlefalse -% \setcornerrules - \else\ifodd\pageno\rightheadline\else\leftheadline\fi\fi \vfill} -\vbox to \pageheight{ - \ifvoid\margin\else - \rlap{\kern31pc\vbox to0pt{\kern4pt\box\margin \vss}}\fi - #1 % -\ifvoid\footins\else - \vskip\skip\footins \kern 0pt - \hrule height\ruleht width 2.5pc \kern-\ruleht \kern 0pt - \unvbox\footins\fi -\boxmaxdepth=\maxdepth}} -\advancepageno} - -\def\setcornerrules{\hbox to \pagewidth{ - \vrule width 1pc height\ruleht \hfil \vrule width 1pc} - \hbox to \pagewidth{\llap{\sevenrm(page \folio)\kern1pc} - \vrule height1pc width\ruleht depth0pt - \hfil \vrule width\ruleht depth0pt}} -\output{\onepageout{\unvbox255}} - -\newbox\partialpage -\def\begindoublecolumns{\begingroup - \output={\global\setbox\partialpage=\vbox{\unvbox255\bigskip}}\eject - \output={\doublecolumnout} \hsize=20pc \vsize=101pc} -\def\enddoublecolumns{\output={\balancecolumns}\eject - \endgroup \pagegoal=\vsize} - -\def\doublecolumnout{\splittopskip=\topskip \splitmaxdepth=\maxdepth - \dimen@=50pc \advance\dimen@ by-\ht\partialpage - \setbox0=\vsplit255 to\dimen@ \setbox2=\vsplit255 to\dimen@ - \onepageout\pagesofar \unvbox255 \penalty\outputpenalty} -\def\pagesofar{\unvbox\partialpage - \wd0=\hsize \wd2=\hsize \hbox to\pagewidth{\box0\hfil\box2}} -\def\balancecolumns{\setbox0=\vbox{\unvbox255} \dimen@=\ht0 - \advance\dimen@ by\topskip \advance\dimen@ by-\baselineskip - \divide\dimen@ by2 \splittopskip=\topskip -{\vbadness=10000 \loop \global\setbox3=\copy0 - \global\setbox1=\vsplit3 to\dimen@ - \ifdim\ht3>\dimen@ \global\advance\dimen@ by1pt \repeat} - \setbox0=\vbox to\dimen@{\unvbox1} \setbox2=\vbox to\dimen@{\unvbox 3} -\pagesofar} - - - - -% Turn off @ as being a letter. -% -\catcode`\@=13 - -% End of ptexpprt.sty - - -CUT HERE............ diff --git a/Master/texmf-dist/tex/amstex/siam/amsamp.tex b/Master/texmf-dist/tex/amstex/siam/amsamp.tex deleted file mode 100644 index 44048937dd7..00000000000 --- a/Master/texmf-dist/tex/amstex/siam/amsamp.tex +++ /dev/null @@ -1,365 +0,0 @@ -% This is the sample paper for the AmSTeX SIAM style file, (amstex)siam.sty -% for use with AmSTeX version 2.1 or later and amsppt.sty, version 2.1a. -% RCS information: $Revision: 1.1 $, $Date: 93/01/25 15:33:19 $. -\input amstex -\documentstyle{amstexs1} -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% Macro definitions for running heads and first page % -\accepted\SIMAF % -\firstpageno{10} % -\lastpageno{12} % -\issuevolume{1} % -\issuenumber{2} % -\issuemonth{February} % -\placenumber{002} % place of paper in this issue % -\issueyear{1988} % -\shortauthor{Bradley J. Lucier and Douglas N. Arnold} % -\shorttitle{A Sample Paper} % -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% Macros specific to this paper % -\define\loner{{L^1(\Bbb R)}} % -\define\linfr{{L^\infty(\Bbb R)}} % -\define\bvr{{\roman{BV}(\Bbb R)}} % -\define\TV{{\roman {TV}}} % -\define\sdot{\,\cdot\,} % -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\topmatter -\title -A SAMPLE PAPER, WITH A RATHER LONG TITLE, TO ILLUSTRATE THE -\AmSTeX\ SIAM STYLE\footnote[\boldkey*]{Unlikely to appear.} -\endtitle -\author -BRADLEY J. LUCIER\footnote[\dag]{Department of Mathematics, Purdue University, -West Lafayette, Indiana 47907. Present address, somewhere on the beach -(lucier\@math.purdue.edu). -The work of the first author was not supported by the -Wolf Foundation.}\ and DOUGLAS N. ARNOLD\footnote[\ddag]{Department -of Mathematics, Pennsylvania State University, -University Park, Pennsylvania 16802.} -\endauthor -\abstract -This sample paper illustrates many of the amstex -macros as used with the \AmSTeX\ SIAM style file amstexsiam (version 2.0a). -The \AmSTeX\ SIAM style file, which -inputs and builds upon the amsppt style (version 2.1a or later) -of Michael Spivak, gives authors easy -access to most of the typographical constructions used in SIAM journals. -It does not address the issues of the table of contents -or tables, which must be set using more primitive \TeX\ macros. -\endabstract -\keywords -porous medium, interface curves -\endkeywords -\subjclass -65N60 -\endsubjclass -\endtopmatter -\document -\subhead 1. Introduction\endsubhead -We are concerned with numerical approximations to the so-called -porous-medium equation \cite{6}, -$$ -\alignedat2 - &u_t=\phi(u)_{xx},&&\qquad x\in\Bbb R,\quad t>0,\quad\phi(u)=u^m,\quad m>1, -\\ - &u(x,0)=u_0(x),&&\qquad x\in\Bbb R. -\endalignedat -\tag 1.1 -$$ -We assume that the initial data $u_0(x)$ has bounded support, that -$0\leq u_0\leq M$, and that $\phi(u_0)_x\in\bvr$. -It is well known that a unique solution $u(x,t)$ of (1.1) exists, -and that $u$ satisfies -$$ - 0\leq u\leq M\text{ and }\TV\phi(u(\,\cdot\,,t))_x\leq\TV\phi(u_0)_x. -\tag 1.2 -$$ -If the data has slightly more regularity, then this too is satisfied -by the solution. Specifically, if $m$ is no greater than two and -$u_0$ is Lipschitz continuous, then $u(\,\cdot\,,t)$ is also Lipschitz; -if $m$ is greater than two and $(u_0^{m-1})_x\in\linfr$, then -$(u(\,\cdot\,,t)^{m-1})_x\in\linfr$ -(see [3]). (This will follow from results presented here, also.) -We also use the fact that the solution $u$ is H\"older continuous in $t$. - -\subhead 2. $\linfr$ error bounds\endsubhead -After a simple definition, we state a theorem -that expresses the error of approximations $u^h$ in -terms of the weak truncation error $E$. -\definition{Definition 2.1}\rm A {\it definition} -is the same as a theorem set in roman -type. In version 2 of the \AmSTeX\ style file for the SIAM journals, -definitions are set with their own command. -\enddefinition -\proclaim{Theorem 2.1} -Let $\{u^h\}$ be a family of approximate solutions satisfying -the following conditions for $0\leq t\leq T${\rm:} -\roster -\item For all $x\in\Bbb R$ and positive $t$, $0\leq u^h(x,t)\leq M${\rm;} -\item Both $u$ and $u^h$ are H\"older--$\alpha$ in $x$ -for some $\alpha\in(0,1\wedge 1/(m-1))${\rm;} $u^h$ is right -continuous in $t${\rm;} -and $u^h$ is H\"older continuous in $t$ on -strips $\Bbb R\times(t^n,t^{n+1})$, with the set $\{t^n\}$ having no -limit points\/{\rm;} and -\item There exists a positive function $\omega(h,\epsilon)$ such that\/{\rm:} -whenever $\{w^\epsilon\}_{0<\epsilon\leq\epsilon_0}$ is a family of functions -in $\bold X$ for which -{\roster -\item"(a)" there is a sequence of positive numbers $\epsilon$ tending -to zero, such that for these values of -$\epsilon$, $\|w^\epsilon\|_\infty\leq 1/\epsilon$, -\item"(b)" for all positive -$\epsilon$, $\|w_x^\epsilon(\sdot,t)\|_\loner\leq 1/\epsilon^2$, and -\item"(c)" for all $\epsilon>0$, -$$ -\sup\Sb -x\in\Bbb R\\0\leq t_1,t_2\leq T\endSb -\dfrac{|w^\epsilon(x,t_2)-w^\epsilon(x,t_1)|}{|t_2-t_1|^p}\leq 1/\epsilon^2, -$$ -where $p$ is some number not exceeding $1$, -\endroster}% -then\footnote{This is an obvious ploy, but we need a footnote.} - $|E (u^h,w^\epsilon,T)|\leq\omega(h,\epsilon).$ -\item -This is the fourth item in the outer roster. -\endroster -Then, there is a constant $C=C(m,M,T)$ such that -$$\multline -\|u-u^h\|_{\infty,\Bbb R\times[0,T]}\leq C\biggl[ -\sup \biggl |\int_\Bbb R(u_0(x)-u^h(x,0)) w(x,0) \,dx\biggr|\\ -+\omega(h,\epsilon)+\epsilon^\alpha\biggr],\endmultline -\tag 2.1 -$$ -where the supremum is taken over all $w\in\bold X$. -\endproclaim - -\demo{Proof} -We assume first that $Q$ is decreasing and consider the following cases: -\case{Case\/ {\rm1:} -$b'\geq 1/2$} We have $P(1/8)\geq\delta>0$ where $\delta$ -depends only on $d$, for otherwise by (3.7) applied to $P$ and $p=\infty$, -$P$ could not attain the value $1$ at $x=1$. Similarly, for -$m=(a'+b')/2$, $Q(m)\geq\delta'>0$ for some $\delta'$ depending only on $d$ -since otherwise $Q$ cannot attain the value $1$ at $x=a'$. Hence, for -$\delta''=\min(\delta,\delta')$, -$|A(y)|\geq|m-1/8|\geq b'/4\geq\frac18\max(b',1)$ for -$y\in[0,\delta'']$. On the other hand, -$|A(y)|\leq \max(b',1)$ for all $y\in[0,1]$, so (4.2) follows for -all $1\leq p\leq\infty$. -\endcase -\case{Case\/ {\rm2:} -$b'\leq 1/2$} We have $P(3/4)\leq\delta<1$ with $\delta$ -depending only on $d$ for otherwise (3.7) applied to $1-P$ and $p=\infty$ -would show that $P$ could not attain the value $0$ at $x=0$. It follows -that $|A(y)|\geq 3/4-b'\geq 1/4$, $y\in[\delta,1]$, while $|A(y)|\leq 1$ -for all $y\in[0,1]$. Hence (4.2) follows for -all $1\leq p\leq\infty$. -\endcase -We consider now when $Q$ is increasing. We can assume that $Q$ is not -a translate of $P$, i.e\., we do not have $P(x)=Q(x+\delta)$ for some $\delta$, -for then (4.2) follows trivially. In what follows, $C$ and $\delta$ -depend on $d$, and $C$ may depend on $p$. We consider the following cases: -\case{Case\/ {\rm3:} $a'\geq 1/4$ and $b'\leq 100$} -From (3.7) for $P$ -and $p=\infty$, it follows that $P(1/8)\geq\delta$ since otherwise $P$ cannot -attain the value $1$ at $x=1$. Hence $|A(y)|\geq a'-1/8\geq1/8$ on -$[0,\delta]$. On the other hand $|A(y)|\leq b'$ for all $y\in[0,1]$ and hence -(4.2) follows for all $1\leq p\leq\infty$. -\endcase -Let $z$ be in $\bold X$. Because $E(u,\sdot,\sdot)\equiv0$, -Equation (1.5) implies that -$$ -\int_\Bbb R\Delta uz|^T_0dx=\int_0^T\int_\Bbb R -\Delta u(z_t+\phi[u,u^h]z_{xx})\,dx\,dt- -E(u^h,z,t), -\tag 2.2 -$$ -where $\Delta u=u-u^h$ and -$$ -\phi[u,u^h]=\dfrac{\phi(u)-\phi(u^h)}{u-u^h}. -$$ -Extend $\phi[u,u^h](\cdot,t)=\phi[u,u^h](\cdot,0)$ for negative $t$, and -$\phi[u,u^h](\cdot,t)=\phi[u,u^h](\cdot,T)$ -for $t>T$. -Fix a point $x_0$ and a number $\epsilon>0$. Let $j_\epsilon$ -be a smooth function of $x$ with integral $1$ and support in -$[-\epsilon,\epsilon]$, -and let $J_\delta$ be a smooth function of -$x$ and $t$ with integral $1$ and support in -$[-\delta,\delta]\times[-\delta,\delta]$; $\delta$ and $\epsilon$ are -positive numbers to be specified later. -We choose $z=z^{\epsilon\delta}$ to satisfy -$$ -\aligned - &z_t+(\delta+J_\delta*\phi[u,u^h])z_{xx}=0,\qquad x\in\Bbb R,\;0 -\leq t\leq T,\\ - &z(x,T)=j_\epsilon(x-x_0). -\endaligned -\tag 2.3 -$$ -The conclusion of the theorem now follows from (2.1) and the fact that -$$ -|j_\epsilon*\Delta u(x_0,t)-\Delta u(x_0,t)|\leq C\epsilon^\alpha, -$$ -which follows from Assumption 2. -\qquad\qed -\enddemo -\example{Example\/ {\rm 1}} This is an example of an example. -\endexample -\remark{Remark\/ {\rm 1}} Examples are set the same as definitions in -some styles, -and the same as proofs in others. What convention does this style follow? -\endremark -Sometimes you want to include a figure, as in Fig.~1. -\topinsert -\def\Bif{{\bf if\/ }}\def\Bwhile{{\bf while\/ }}\def\Belse{{\bf else\/ }} -\settabs\+\qquad&\qquad&\qquad&\qquad&\cr -\+\smc Tree Partition Algorithm \{\cr -\+&Let stack size denote the number of nodes in the\cr -\+&&subtrees stored temporarily on the local stack\cr -\+&pop I from global stack\cr -\+&set stack size := 0\cr -\+&\Bwhile (stack size $\leq$ max size and stack size + -I$\rightarrow$tree size $>$ 3 (max size)) \{\cr -\+&&process I as an interior node\cr -\+&&let min tree be the smaller of the subtrees of the two children of I\cr -\+&&let max tree be the larger of the subtrees of the two children of I\cr -\+&&\Bif (min tree$\rightarrow$tree size + stack size $>$ 3 (max size)) \{\cr -\+&&&push min tree onto the global stack\cr -\+&&\} \Belse \{\cr -\+&&&push min tree onto the local stack\cr -\+&&&set stack size := stack size + min tree$\rightarrow$tree size\cr -\+&&\}\cr -\+&&set I := max tree\cr -\+&\}\cr -\+&\Bif (I$\rightarrow$tree size + stack size $>$ 3 (max size)) \{\cr -\+&&push I onto the global stack\cr -\+&\} \Belse \{\cr -\+&&push I onto the local stack\cr -\+&\}\cr -\+&Process all subtrees on the local stack\cr -\+\}\cr -\botcaption{Fig.~1} Tree partition algorithm Tree partition algorithm -Tree partition algorithm Tree partition algorithm Tree partition algorithm -Tree partition algorithm Tree partition algorithm.\endcaption -\endinsert - -We finish with a table of all SIAM journals. -\midinsert -\topcaption{Table 1}{SIAM journal acronyms and titles}\endcaption -\settabs\+\indent&Acronym\indent&Title&\cr -\hbox to \hsize{\hrulefill} -\+&Acronym&Title&\cr -\hbox to \hsize{\hrulefill} -\+&SINUM&SIAM Journal on Numerical Analysis&\cr -\+&SIREV&SIAM Review&\cr -\+&SIMA&SIAM Journal on Mathematical Analysis&\cr -\+&SIMAX&SIAM Journal on Matrix Analysis and Applications&\cr -\+&SICOMP&SIAM Journal on Computing&\cr -\+&SISC&SIAM Journal on Scientific Computing&\cr -\+&SIOPT&SIAM Journal on Optimization&\cr -\+&SIAP&SIAM Journal on Applied Mathematics&\cr -\+&SICON&SIAM Journal on Control and Optimization&\cr -\+&SIDMA&SIAM Journal on Discrete Mathematics&\cr -\+&TVP&Theory of Probability and Its Applications&\cr -\hbox to \hsize{\hrulefill} -\endinsert - -\Refs -\ref - \no 1 - \by L. A. Caffarelli and A. Friedman - \paper Regularity of the free boundary of a gas flow in an - $n$-dimensional porous medium - \jour Indiana Math. J. - \vol 29 - \yr 1980 - \pages 361--391 -\endref -\ref\no 2 - \by R. DeVore and B. Lucier - \paper High order regularity for solutions of the inviscid Burgers equation - \inbook Nonlinear Hyperbolic Problems -\procinfo Proceedings of an Advanced Research Workshop, Bordeaux, -France, June 1988 - \bookinfo Lecture Notes in Mathematics - \vol 1402 - \eds C. Carasso, P. Charrier, B. Hanouzet, and J.-L. Joly - \yr 1989 - \publ Springer-Verlag - \publaddr New York - \pages 147--154 -\endref -\ref \no 3 - \bysame - \paper Wavelets - \jour Acta Numerica - \yr 1992 - \ed A. Iserles - \publ Cambridge University Press - \publaddr New York - \pages 1--56 -\endref -\ref \no 4 - \by R. A. DeVore and V. A. Popov - \paper Interpolation spaces and non-linear approximation - \inbook Function Spaces and Applications - \bookinfo Lecture Notes in Mathematics - \procinfo Proceedings of the US--Swedish Seminar held in Lund, -Sweden, June 15--21, 1986 - \vol 1302 - \eds M. Cwikel, J. Peetre, Y. Sagher, and H. Wallin - \publ Springer-Verlag - \publaddr New York - \yr 1988 - \pages 191--205 - \endref -\ref \no 5 - \by R. A. DeVore and X. M. Yu - \paper Nonlinear $n$-widths in Besov spaces - \inbook Approximation Theory VI: Vol. 1 - \eds C. K. Chui, L. L. Schumaker, and J. D. Ward - \publ Academic Press - \publaddr New York - \yr 1989 - \pages 203--206 - \lang In Russian - \endref -\ref - \no 6 - \by K. Hollig and M. Pilant - \paper Regularity of the free boundary for the porous medium equation - \paperinfo MRC Tech. Rep. 2742 -\endref -\ref - \no 7 - \by J. Jerome - \book Approximation of Nonlinear Evolution Systems - \publ Academic Press - \publaddr New York - \yr 1983 -\endref -\ref - \no 8 - \manyby R. J. LeVeque - \paper Convergence of a large time step generalization of Godunov's method - for conservation laws - \jour Comm. Pure Appl. Math. - \vol 37 - \yr 1984 - \pages 463--478 -\endref -\ref\no 9 - \by O. Rioul and M. Vetterli - \paper Wavelets and signal processing - \jour IEEE Signal Processing Magazine - \vol 8 - \issue 4 - \yr 1991 - \toappear -\endref -\endRefs -\enddocument - diff --git a/Master/texmf-dist/tex/amstex/siam/amstexsi.sty b/Master/texmf-dist/tex/amstex/siam/amstexsi.sty deleted file mode 100644 index 4ba461dc9dc..00000000000 --- a/Master/texmf-dist/tex/amstex/siam/amstexsi.sty +++ /dev/null @@ -1,634 +0,0 @@ -%% This is amstexsiam.sty, the AmS-TeX SIAM style file. This file -%% should be accompanied by the sample paper, siamsamp.tex, and the -%% documentation file, siamdoc.tex. -%% -%% This is version 2.1 of November 1995. -%% -%% Authors: -%% -%% Prof. Bradley Lucier -%% Department of Mathematics -%% 1395 Mathematical Sciences Building -%% Purdue University -%% West Lafayette, IN 47907-1395 -%% lucier@math.purdue.edu -%% -%% Prof. Douglas N. Arnold -%% Department of Mathematics -%% Penn State University -%% University Park, PA 16802 -%% dna@math.psu.edu -%% -%% Copyright 1988, 1990, 1993, 1995 by Bradley Lucier. All rights reserved. -%% You have permission to copy this file, to use it as input to other TeX -%% files, and to modify it as necessary to allow it to run at your site. -%% In the interest of maintaining a consistent revision history, if you -%% make changes, additions, or deletions to this file, you must indicate -%% how the changes affected the original file, so that the original file -%% can be reconstructed if necessary. -%% -%% This is an official SIAM style file for AmSTeX, version 2.1. It -%% requires amsppt.sty, version 2.1a. Later versions are probably -%% acceptable. This style file has been used to produce papers for -%% SIAM journals that have been totally acceptable to SIAM production -%% editors. -%% -%% This style file is unsupported. To report bugs, suggest changes, -%% or make other comments, contact the first named author. -%% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% RCS information: $Revision: 1.12 $, $Date: 95/11/20 13:11:59 $. -\def\filename{amstexsiam.sty} -\def\fileversion{2.1} -\def\filedate{November 1995} -\message{version \fileversion\space(\filedate):} -\def\styname{AMSTEXSIAM}\def\styversion{2.1} -% -% We save the catcode of @ before we call amsppt.sty, since amsppt.sty -% redefines \filename. -% -\expandafter\xdef\csname\filename\endcsname{% - \catcode`\noexpand\@=\the\catcode`\@ - \expandafter\gdef\csname\filename\endcsname{% - \fileversion\space(\filedate)}} -% -\input amsppt.sty -% -\catcode`\@=11 -% -% Change the crucial dimensions. We use 20pt instead of 2 em for -% the \parindent, because at one point we want to set it to the same thing -% in \eightpoint, and 2 em in \eightrm is smaller than 2 em in \tenrm. -% I removed every instance of em in this style file---it was used in the -% setting of item numbers in rosters, and in the indentation of references. -% I substituted 10 pts for it. -% -\def\pagewidth#1{\hsize#1\captionwidth@\hsize} -\pagewidth{31 pc} \hcorrection{0.6666666 in} -\pageheight{49.5 pc} \vcorrection{0.3333333 in} -\topskip 12pt -\parindent 20pt -\parskip 0 pt -% -% change the space above and below displayed equations to 6 + 3 pts. -% SIAM style is 6 pts. I also added a call to \rm to override the -% call to \eightrm in \eightpoint in case anyone ever wants to redefine the -% text fonts for \eightpt -\addto\tenpoint{\abovedisplayskip 6\p@ plus 3\p@ - \belowdisplayskip\abovedisplayskip - \abovedisplayshortskip 0 \p@ plus 3\p@ - \belowdisplayshortskip\belowdisplayskip} -\addto\eightpoint{\abovedisplayskip 6\p@ plus 3\p@ - \belowdisplayskip\abovedisplayskip - \abovedisplayshortskip 0 \p@ plus 3\p@ - \belowdisplayshortskip\belowdisplayskip\rm} -% -% various amsppt macros are not to be used in the amstexsiam style file -% -\def\taboo@#1{\def#1{% - \errmessage{Do not use \string#1 in the amstexsiam style; see the instructions.}}} -\taboo@\thanks\taboo@\endthanks % use the title footnote. -\taboo@\preaffil\taboo@\affil\taboo@\endaffil % use the author footnotes -\taboo@\address\taboo@\endaddress % use the author footnotes -\taboo@\predate\taboo@\date\taboo@\enddate % use the title footnote. -\taboo@\email\taboo@\endemail % use the author footnotes -% -% Changes to the topmatter. (Differences refer to amsppt.sty, version 2.1a) -% -% We don't increase the line spacing in the title, we don't uppercase, -% we record the depth of the last line for use in \endtopmatter. -% -\newdimen\titledepth@ -\def\title#1\endtitle{\global\setbox\titlebox@ - \vtop{\bgroup\tenpoint\bf\raggedcenter@ - #1\endgraf\global\titledepth@\prevdepth\egroup}\relaxnext@} -% -% \author uses small caps, otherwise is like title. -% -\newdimen\authordepth@ -\def\author#1\endauthor{\global\setbox\authorbox@ - \vtop{\bgroup\eightpoint\smc\raggedcenter@ - #1\endgraf\global\authordepth@\prevdepth\egroup}\relaxnext@} -% -% Abstract: don't change the left and right skips, do indent, -% don't put the thing in displayed math, change the -% font from small cap to bold for "Abstract". Remember the depth of -% the last line in abstract for \endtopmatter. -% -\newdimen\abstractdepth@ -\def\abstract{\let\savedef@\abstract - \def\abstract{\let\abstract\savedef@ - \setbox\abstractbox@\vtop\bgroup - \def\envir@end{\endabstract} - \def\usualspace{\enspace}\eightpoint\indent - \frills@{{\bf Abstract.\enspace}}}% - \nofrillscheck\abstract} -\def\endabstract{\endgraf\global\abstractdepth@\prevdepth\unskip\egroup} -% -% Add keywords and subject classifications just like the abstract. -% -\def\prekeywords{} -\newbox\keywordsbox@ -\newdimen\keywordsdepth@ -\def\keywords{\let\savedef@\keywords - \def\keywords{\let\keywords\savedef@ - \setbox\keywordsbox@\vtop\bgroup - \def\envir@end{\endkeywords} - \def\usualspace{\enspace}\eightpoint\indent - \frills@{{\bf Key words.\enspace}}}% - \nofrillscheck\keywords} -\def\endkeywords{\endgraf\global\keywordsdepth@\prevdepth\unskip\egroup} -\def\presubjclass{} -\newbox\subjclassbox@ -\newdimen\subjclassdepth@ -\def\subjclass{\let\savedef@\subjclass - \def\subjclass{\let\subjclass\savedef@ - \setbox\subjclassbox@\vtop\bgroup - \def\envir@end{\endsubjclass} - \def\usualspace{\enspace}\eightpoint\indent - \frills@{{\bf AMS subject classifications.\enspace}}}% - \nofrillscheck\subjclass} -\def\endsubjclass{\endgraf\global\subjclassdepth@\prevdepth\unskip\egroup} -% -% Amazingly enough, we get the spacing perfectly correct; however, if -% any one part of the topmatter should need to cross a page boundary, -% then we are in trouble, since we leave each part of the topmatter in a -% \vbox, and things will have to be set by hand. (amsppt.sty has the same -% problem if the abstract should cross a page boundary.) -% After adding each part of the topmatter -% we change \prevdepth to reflect the depth of the last line of each part. -% -\outer\def\endtopmatter{\add@missing\endabstract - \add@missing\endkeywords\add@missing\endsubjclass - \pretitle - \begingroup % to localize variant topskip - \topskip 3pc\advance\topskip by -\ht\titlebox@ - \null\unvbox\titlebox@ - \prevdepth\titledepth@ - \endgroup - \preauthor - \ifvoid\authorbox@\else - \baselineskip 18 pt\advance\baselineskip by -\ht\authorbox@ - \null\unvbox\authorbox@\prevdepth\authordepth@\fi - \preabstract - \ifvoid\abstractbox@\else - \baselineskip 24 pt\advance\baselineskip by -\ht\abstractbox@ - \null\unvbox\abstractbox@\prevdepth\abstractdepth@\fi - \prekeywords - \ifvoid\keywordsbox@\else - \baselineskip 20 pt\advance\baselineskip by -\ht\keywordsbox@ - \null\unvbox\keywordsbox@\prevdepth\keywordsdepth@\fi - \presubjclass - \ifvoid\subjclassbox@\else - \baselineskip 20 pt\advance\baselineskip by -\ht\subjclassbox@ - \null\unvbox\subjclassbox@\prevdepth\subjclassdepth@\fi - \ifvoid\tocbox@\else\vskip1.5pcplus.5pc\unvbox\tocbox@\fi - \prepaper - \vskip 8 pt % The first line of the paper body will be set with 12 pt - % baselines, so this extra 8 points will make it 20 pts total. - \tenpoint\relax -} -% -% Simplify it, since we don't add a lot of things at the end of the -% document like amsppt does. -% -\outer\def\enddocument{\par% \par will do a runaway check for \endref - \add@missing\endRefs - \add@missing\endroster \add@missing\endproclaim - \add@missing\enddefinition - \add@missing\enddemo \add@missing\endremark \add@missing\endexample - \vfill\supereject\end} -% -% We add a thin space between the footnotemark and the footnotetext. -% -% We also undo \raggedcenter@ inside the foonote. -% -\def\undoraggedcenter@{\leftskip\z@\rightskip\z@\parfillskip0ptplus1fil% - \parindent20pt\spaceskip0\p@\xspaceskip0\p@\pretolerance100% - \tolerance200\exhyphenpenalty50\hyphenpenalty50} -\def\makefootnote@#1#2{\insert\footins - {\interlinepenalty\interfootnotelinepenalty -\eightpoint\undoraggedcenter@\splittopskip\ht\strutbox\splitmaxdepth\dp\strutbox - \floatingpenalty\@MM\leavevmode{#1}\,\footstrut - \ignorespaces#2\unskip\lower\dp\strutbox - \vbox to\dp\strutbox{}}} -% -% The skip before a heading is 6 pts, no stretchiness -% -\subheadskip 6 pt -% -% -% the amsppt monograph style has the same indentation rules as the SIAM -% style. -% -\let\varindent@\indent -% -% Proclaims use small caps. -% -\def\proclaimheadfont@{\smc} -% -% Now we have to change a lot of things because Spivak put \medskipamounts -% before and after proclaims, etc. Perhaps he should have defined and used -% \varskipamount@ like varindent@ and then we would have had to change only -% one line. (Hint, hint!) To keep things simple, I just changed the -% \medskipamounts to 0pt in the following, even though it doesn't make -% total sense to do so. -% -% Next line needed since it was previously defined outer. -% -\let\proclaim\relax -\outer\def\proclaim{% - \let\savedef@\proclaim \let\proclaim\relax - \add@missing\endroster \add@missing\enddefinition - \add@missing\endproclaim \envir@stack\endproclaim - \def\proclaim##1{\restoredef@\proclaim - \penaltyandskip@{-100}{0pt}\varindent@ - \def\usualspace{{\proclaimheadfont@\enspace}}\proclaimheadfont@ - \ignorespaces##1\unskip\frills@{.\enspace}% - \it\ignorespaces}% - \nofrillscheck\proclaim} -\def\endproclaim{\revert@envir\endproclaim \par\rm - \penaltyandskip@{55}{0pt}} -\def\remark{\let\savedef@\remark \let\remark\relax - \add@missing\endroster \add@missing\endproclaim - \envir@stack\endremark - \def\remark##1{\restoredef@\remark - \penaltyandskip@\z@{0pt} - {\def\usualspace{{\remarkheadfont@\enspace}}% - \varindent@\remarkheadfont@\ignorespaces##1\unskip - \frills@{.\enspace}}\rm - \ignorespaces}\nofrillscheck\remark} -\def\definition{\let\savedef@\definition \let\definition\relax - \add@missing\endproclaim \add@missing\endroster - \add@missing\enddefinition \envir@stack\enddefinition - \def\definition##1{\restoredef@\definition - \penaltyandskip@{-100}{0pt} - {\def\usualspace{{\proclaimheadfont@\enspace}}% - \varindent@\proclaimheadfont@\ignorespaces##1\unskip - \frills@{.\proclaimheadfont@\enspace}}% - \rm \ignorespaces}% - \nofrillscheck\definition} -\def\enddefinition{\revert@envir\enddefinition\par} -\def\enddemo{\par\revert@envir\enddemo \endremark} -% -% Examples are set the same as remarks in the SIAM style. -% -\def\example{\DN@{\ifx\next\nofrills - \DN@####1####2{\remark####1{####2}\envir@stack\endexample - \ignorespaces}% - \else - \DN@####1{\remark{####1}\envir@stack\endexample\ignorespaces}% - \fi - \next@}% -\FN@\next@} -\def\endexample{\par\revert@envir\endexample \endremark} -% -% We will add a \case ... \endcase macro -% -\def\case{\DN@{\ifx\next\nofrills - \DN@####1####2{\remark####1{####2}\envir@stack\endcase - \ignorespaces}% - \else - \DN@####1{\remark{####1}\envir@stack\endcase\ignorespaces}% - \fi - \next@}% -\FN@\next@} -\def\endcase{\par\revert@envir\endcase \endremark} -% -% Remarks, proofs, etc. have the first word in italic. -% -\def\remarkheadfont@{\it} -% -% Redefine \qed -% -\def\qed{\ifhmode\unskip\nobreak\fi\ifmmode\ifinner\else\hskip5\p@\fi\fi - \hbox{\hskip25\p@ minus 10 \p@\hbox{\vrule width .6\p@\vbox{\hrule width 4\p@ - height .6\p@\vskip 6.2\p@\hrule width 4\p@ height .6\p@}\unskip\vrule - width .6\p@}\hskip\p@}} -% -% We should deal somewhat with table and figure legends. Unfortunately, -% they differ in several key respects from the amsppt style. Tables have -% "Table 1" in small caps centered on first line of caption, table -% description centered in italics on following lines. Legend has "Fig. 1." -% in smc followed by description in italic. -% -\def\topcaption#1#2\endcaption{% - \eightpoint{\dimen@\hsize \advance\dimen@-\captionwidth@ - \it\raggedcenter@ \advance\leftskip.5\dimen@ \rightskip\leftskip - {\captionfont@#1}% - \if\notempty{#2}\\\ignorespaces#2\fi - \endgraf}\nobreak\smallskip} -\def\botcaption#1#2\endcaption{% - \nobreak\medskip - \eightpoint\setboxz@h{\captionfont@#1\if\notempty{#2}.\enspace\it#2\fi}% - {\dimen@\hsize \advance\dimen@-\captionwidth@ - \leftskip.5\dimen@ \rightskip\leftskip - \noindent \ifdim\wdz@<\captionwidth@ - \hfil{\captionfont@#1}\if\notempty{#2}.\enspace\it#2\fi\hfil - \else - \par{\captionfont@#1}% - \if\notempty{#2}.\enspace\it#2\fi\endgraf\fi}} -\def\@ins{\par\begingroup\def\vspace##1{\vskip##1\relax}% - \def\captionwidth##1{\captionwidth@##1\relax}% - \setbox\z@\vbox\bgroup} % start a \vbox -% -% We remove the smallskip before rosters and change them to not use hang -% indents. -% -\rosteritemwd20pt -\newdimen\rosteritemindent@ -\rosteritemindent@-20pt -\def\roster{% - \envir@stack\endroster - \global\advance\rosteritemindent@ by 20 pt - \edef\leftskip@{\leftskip\the\leftskip}% - \relaxnext@ - \rostercount@\z@ - \def\item{\FN@\rosteritem@}% - \DN@{\ifx\next\runinitem\let\next@\nextii@\else - \let\next@\nextiii@\fi\next@}% - \DNii@\runinitem% - {\unskip% - \DN@{\ifx\next[\let\next@\nextii@\else - \ifx\next"\let\next@\nextiii@\else\let\next@\nextiv@\fi\fi\next@}% - \DNii@[####1]{\rostercount@####1\relax - \enspace\therosteritem{\number\rostercount@}~\ignorespaces}% - \def\nextiii@"####1"{\enspace{\rm####1}~\ignorespaces}% - \def\nextiv@{\enspace\therosteritem1\rostercount@\@ne~}% - \par@\firstitem@false% - \FN@\next@}% - \def\nextiii@{\par\par@ - \penalty\@m - \firstitem@true} - \FN@\next@} -\def\rosteritem@{\iffirstitem@\firstitem@false - \else\par\vskip-\parskip\fi - \leftskip\rosteritemindent@\noindent - \DNii@[##1]{\rostercount@##1\relax\itembox@}% - \def\nextiii@"##1"{\def\therosteritem@{\rm##1}\itembox@}% - \def\nextiv@{\advance\rostercount@\@ne\itembox@}% - \def\therosteritem@{\therosteritem{\number\rostercount@}}% - \ifx\next[\let\next@\nextii@\else\ifx\next"\let\next@\nextiii@\else - \let\next@\nextiv@\fi\fi\next@} -% -% We change itembox to do what it should -% -\def\itembox@{\hskip\parindent\hbox to \rosteritemwd{\hss\kern\z@\therosteritem@\enspace}\ignorespaces} -% -% We change the default roster indent to 20 pt (from 16), and remove the -% "\global\rosteritemwd16pt" from \endroster. This allows us to use -% nested rosters in an easy way. -% -\def\endroster{\relaxnext@\revert@envir\endroster\par - \global\advance\rosteritemindent@ by -20 pt - \leftskip@\penalty-50 - \DN@{\ifx\next\Runinitem\let\next@\relax\else\nextRunin@false - \let\item\plainitem@\ifx\next\par\DN@\par{\everypar - \expandafter{\the\everypartoks@}}\else\DN@{\noindent\everypar - \expandafter{\the\everypartoks@}}\fi\fi\next@}\FN@\next@} -% -% References: -% -% We change the word "REFERENCES" to 8 pt roman, and add 28 pt skip -% and a \goodbreak above "REFERENCES" and 8 pt skip and \nobreak below. -% -\let\Refs\relax -\outer\def\Refs{\add@missing\endroster \add@missing\endproclaim - \let\savedef@\Refs \let\Refs\relax % because of \outer-ness - \def\Refs##1{\restoredef@\Refs - \goodbreak\vskip 28 pt - \hbox to\hsize{\hfil\refsfont@\rm - \ignorespaces##1\unskip\hfil}\nobreak - \vskip 8pt - \begingroup\def\envir@end{\endRefs}\refsfont@\sfcode`\.\@m - }% - \nofrillscheck{\csname Refs\expandafter\endcsname - \frills@{{REFERENCES}}}} -% -% Author names are in small caps. -% -\def\by{\makerefbox\by\bybox@\smc} -% -% When we redefine \by, we have to re`let' \manyby. -% -\let\manyby\by -% -% Removed the \thinspace between the rule and the comma, raised -% it by a point, and made it .2 pts thick. -% -\def\bysame{\by\hbox to 30pt{\leaders\hrule height 1.2pt depth -1pt\hfill}} -% -% \ed and \eds are kind of funny; the \edbox@ is used as the \bybox@ -% if there is no \bybox@; the instructions will have to say to use -% \ed or \eds after \by in each reference. -% -\def\ed{\makerefbox\ed\edbox@{\ifvoid\bybox@\smc\fi}} -\def\eds{\gdef\edtext{eds.}\makerefbox\eds\edbox@{\ifvoid\bybox@\smc\fi}} -% -% Paper names are in italics. -% -\def\paper{\makerefbox\paper\paperbox@\it} -% -% The volume number is always roman in the SIAM style. -% -\def\vol{\makerefbox\vol\volbox@\empty} -% -% The SIAM style does not use "no." before the issue, or v. before -% the volume, even in a book. -% -\def\defaultreftexts{\gdef\edtext{ed.}\gdef\pagestext{pp.}} -% -% second and following lines in references are indented 20 pt more than first. -% -\def\ref{\par - \begingroup \def\envir@end{\endref}% - \advance\refindentwd 20 pt\noindent\hangindent\refindentwd - \advance\refindentwd-20 pt - \def\par{\add@missing\endref}% - \global\let\nofrills@list\empty - \refbreaks - \procpaper@false \book@false - \def\curbox{\z@}\setbox\z@\vbox\bgroup -} -% -% We change the reference styles for keys and numbers to be the same; -% the number contained in square brackets followed by an enspace. -% -\def\refstyle#1{\uppercase{% - \if#1A\relax \def\keyformat##1{\hfil[##1]\enspace}% - \else\if#1B\relax - \def\keyformat##1{\aftergroup\kern - \aftergroup-\aftergroup\refindentwd}% - \refindentwd\parindent - \else\if#1C\relax - \def\keyformat##1{\hfil[##1]\enspace}% - \fi\fi\fi}% end of \uppercase -} -% -% Here I am at a loss. The early, inscrutable part of endref@ is, of -% course, from amsppt 2.1a, so see amsppt.doc for the documentation. -% The latter part (Case 1: etc.), just tries to put things into -% their correct place with their correct spacing and surrounding punctuation -% and words (ed., etc.). The changes from amsppt to siam are too numerous to -% list; again, compare this code to amsppt.doc -% -\def\endref@{% - \keyhook@ - \def\nofrillscheck##1{% - \def\do####1{\ifx##1####1\let\frills@\eat@\fi}% - \let\frills@\identity@ \nofrills@list}% - \ifvoid\bybox@ - \ifvoid\edbox@ - \else\setbox\bybox@\hbox{\unhbox\edbox@\breakcheck - \nofrillscheck\edbox@\frills@{\smc, \edtext}\refbreak@}\fi - \fi - \ifvoid\keybox@\else\hbox to\refindentwd{% - \keyformat{\unhbox\keybox@}}\fi - \commaunbox@\morerefbox@ - \ppunbox@\empty\empty\bybox@\empty - \ifbook@ % Case 1: \book etc. - \commaunbox@\bookbox@ - \commaunbox@\procinfobox@ - \commaunbox@\bookinfobox@ - \ppunbox@\empty\space\volbox@\empty - \ppunbox@,\space\edbox@{, \edtext}% - \commaunbox@\publbox@ \commaunbox@\publaddrbox@ - \commaunbox@\yrbox@ - \else - \commaunbox@\paperbox@ \commaunbox@\paperinfobox@ - \ifprocpaper@ % Case 2: \paper ... \inbook - \ppunbox@,{ in }\bookbox@\empty - \commaunbox@\procinfobox@ - \commaunbox@\bookinfobox@ - \ppunbox@\empty\space\volbox@\empty - \ppunbox@,\space\edbox@{, \edtext}% - \commaunbox@\publbox@ \commaunbox@\publaddrbox@ - \commaunbox@\yrbox@ - \else % Case 3: \paper ... \jour - \commaunbox@\jourbox@ - \commaunbox@\volbox@ - \commaunbox@\issuebox@ - \ppunbox@\empty{ (}\yrbox@)% - \commaunbox@\publbox@ \commaunbox@\publaddrbox@ - \fi - \fi - \ppunbox@,{ \pagestext~}\pagesbox@\empty - \commaunbox@\finalinfobox@ - \commaunbox@\miscnotebox@ - \finalpunct\ppunbox@\empty{ (}\langbox@)% - \defaultreftexts -} -% -% \iffirstpage@ is defined in amsppt; we make sure it is true. -% -\firstpage@true -% -% We want to avoid people setting papers with the SIAM slug by default. -% We introduce a new macro \accepted that will set a flag to do this. -% -\newif\ifaccepted@ -\def\firstpageno#1{\gdef\firstpageno@{#1}} -\def\lastpageno#1{\gdef\lastpageno@{#1}} -\def\journalname#1{\gdef\journalname@{#1}} -\def\issuevolume#1{\gdef\issuevolume@{#1}} -\def\issuenumber#1{\gdef\issuenumber@{#1}} -\def\issuemonth#1{\gdef\issuemonth@{#1}} -\def\placenumber#1{\gdef\placenumber@{#1}} -\def\issueyear#1{\gdef\issueyear@{#1}} -\def\shorttitle#1{\gdef\shorttitle@{\lowercase{#1}}} -\def\shortauthor#1{\gdef\shortauthor@{\lowercase{#1}}} -\def\accepted{\accepted@true -\journalname{XXXXXXXXXXXXXXXXXX}% -\firstpageno{1}% -\lastpageno{XX}% -\issuevolume{0}% -\issuenumber{0}% -\issuemonth{XXXXXXX}% -\placenumber{000}% -\issueyear{19XX}% -} -\shortauthor{} -\shorttitle{} -\accepted@false -\output={\output@} -% -% The new output@, taken almost verbatim from amstexsiam, version 1.*; -% I changed \oddhead and \evenhead to \shorttitle and \shortauthor---users -% shouldn't really have to check whether the title is on odd or even pages. -% -\def\output@{% -\iffirstpage@\global\firstpage@false\shipout - \vbox{\ifaccepted@\global\pageno=\firstpageno@\vbox to 2 pc - {\baselineskip=8pt\vss - \hbox to \hsize{\sixrm\journalname@\hfill{\textfont\tw@\sixsy - \copyright}\ \issueyear@\ Society for Industrial and Applied Mathematics} - \hbox to \hsize{\sixrm Vol.~\issuevolume@, No.~\issuenumber@, - pp.~\firstpageno@--\lastpageno@, \issuemonth@\ \issueyear@\hfill - \placenumber@}\vskip-\prevdepth\vskip 8 pt}\else\vbox - {\vrule height 2 pc width 0 pt}\fi\nointerlineskip - \vbox to\vsize - {\boxmaxdepth=\maxdepth \pagecontents}\nointerlineskip\vbox to 16 pt{\vss - \hbox to \hsize{\eightpoint\hfill\number\pageno\hfill}}}% - \else - \shipout\vbox{\vbox to 2 pc{\baselineskip=12pt - \vss\ifodd\pageno - \hbox to \hsize{\tenpoint\relaxnext@\phantom{\number\pageno}\hfil - {\smc\frenchspacing{\shorttitle@}}\hfil\number\pageno} - \else - \hbox to \hsize{\tenpoint\number\pageno\hfil{\smc\frenchspacing{\shortauthor@}}\hfil\relaxnext@ - \phantom{\number\pageno}}\fi\vskip-\prevdepth\vskip 12 pt}\nointerlineskip% - \vbox to\vsize - {\boxmaxdepth=\maxdepth \pagecontents}}% changed to resemble TeXBook, p255 PCD - \fi - \global\advance\pageno\@ne - \ifnum\outputpenalty>-\@MM\else\dosupereject\fi} -\def\SIMAF{\journalname{{\sixrm SIAM J. M{\fiverm ATH.} F{\fiverm OOL.}}}}% for sample paper -\def\SIAP{\journalname{{\sixrm SIAM J. A{\fiverm PPL.} M{\fiverm ATH.}}}} -\def\SICOMP{\journalname{{\sixrm SIAM J. C{\fiverm OMPUT.}}}} -\def\SICON{\journalname{{\sixrm SIAM J. C{\fiverm ONTROL} {\fiverm AND} O{\fiverm PTIMIZATION}}}} -\def\SIDMA{\journalname{{\sixrm SIAM J. D{\fiverm ISC.} M{\fiverm ATH.}}}} -\def\SIMA{\journalname{{\sixrm SIAM J. M{\fiverm ATH.} A{\fiverm NAL.}}}} -\def\SIMAX{\journalname{{\sixrm SIAM J. M{\fiverm ATRIX} A{\fiverm NAL.} A{\fiverm PPL.}}}} -\def\SINUM{\journalname{{\sixrm SIAM J. N{\fiverm UMER.} A{\fiverm NAL.}}}} -\def\SIOPT{\journalname{{\sixrm SIAM J. O{\fiverm PTIMIZATION}}}} -\def\SISC{\journalname{{\sixrm SIAM J. S{\fiverm CI.} C{\fiverm OMPUT.}}}} -\def\SIREV{\journalname{{\sixrm SIAM R{\fiverm EVIEW}}}} -%\def\TVP{\journalname{{Theory of Probability and its Applications}}} -% but the slug is so different for this journal that I won't include it. -% -% From amstexsiam version 1.* -% -\def\footnoterule{\hrule width 36 pt height .2 pt\vskip 2.8\p@} -\skip\footins=12 pt plus 18 pt minus 6 pt -% -% We use \key in references by default, with a two digit key width. -% -\refstyle{A} -\widestnumber\key{00} -% -% Centered tags on splits seems to be the default. -% -\CenteredTagsOnSplits -% -% The multlinegap@ is 0pt for the SIAM style. -% -\multlinegap@0pt -% -% Every paper will have at least one bold footnotemark (in the title), -% so we load bold. -\loadbold -% -% Start in 10 pt text. -% -\tenpoint -% -% Reset the catcode of @ and reset amstexsiam.sty to be the version number. -% -\csname amstexsiam.sty\endcsname -% -% Make sure that we endinput here so following lines are not interpreted -% by TeX -% -\endinput -%% -%% End of file `amstexsiam.sty' diff --git a/Master/texmf-dist/tex/amstex/siam/siamdoc.tex b/Master/texmf-dist/tex/amstex/siam/siamdoc.tex deleted file mode 100644 index 1d96c542f77..00000000000 --- a/Master/texmf-dist/tex/amstex/siam/siamdoc.tex +++ /dev/null @@ -1,238 +0,0 @@ -%% This is siamdoc.tex, the documentation file for the AmSTeX SIAM -%% style file. This file should be accompanied by the style file -%% itself, amstexsiam.sty, and the sample paper, siamsample.tex. -%% -%% This is version 2.1 of March 1995. -%% -%% Authors: -%% -%% Prof. Bradley Lucier -%% Department of Mathematics -%% 1395 Mathematical Sciences Building -%% Purdue University -%% West Lafayette, IN 47907-1395 -%% lucier@math.purdue.edu -%% -%% Prof. Douglas N. Arnold -%% Department of Mathematics -%% Penn State University -%% University Park, PA 16802 -%% dna@math.psu.edu -%% -%% This file should be typeset with Plain TeX, not AmS-TeX or LaTeX. -%% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% RCS information: $Revision: 1.5 $ $Date: 95/03/03 13:00:26 $ -\catcode`\@=11 -\ifx\amstexloaded@\undefined\relax\else -\W@{^^JTypeset this file with plain TeX, not AmSTeX.^^J}\end\fi -\catcode`\@=\active -\magnification=\magstephalf -\tolerance=1000 -\def\beginverbatim{\par\begingroup\setupverbatim\doverbatim} -{\catcode`\|=0 \catcode`\\=12 % | is temporary escape character - |obeylines|gdef|doverbatim^^M#1\endverbatim{#1|endgroup}} -\def\setupverbatim{\tentt \obeylines \uncatcodespecials \obeyspaces} -{\obeyspaces\global\let =\ } % let active space = control space -\def\uncatcodespecials{\def\do##1{\catcode`##1=12}\dospecials} -{\catcode`\^^M=13 \gdef\gobblecr{\ifnextchar -{\gobble}{\ignorespaces}}} -{\catcode`\ =\active\gdef\vobeyspaces{\catcode`\ \active \let \xobeysp}} - \def\xobeysp{\leavevmode{} } -\begingroup \catcode `|=0 \catcode `[= 1 -\catcode`]=2 \catcode `\{=12 \catcode `\}=12 -\catcode`\\=12 |gdef|@xverbatim#1\end{verbatim}[#1|end[verbatim]] -|gdef|@sxverbatim#1\end{verbatim*}[#1|end[verbatim*]] -|endgroup -\def\makeother#1{\catcode`#112\relax} -\def\v{\begingroup \tt \uncatcodespecials -\averb} -\def\sverb#1{\def\tempa ##1#1{##1\endgroup}\tempa} -\def\averb{\obeyspaces \frenchspacing \sverb} -\font\textfontii = cmsy10 -\font\eightpt = cmr8 -\def\heading#1{\medskip\noindent{\bf #1.\ }} -\def\AmSTeX{{\textfontii A}\kern-.1667em\lower.5ex\hbox - {\textfontii M}\kern-.125em{\textfontii S}-\TeX} -\def\qed{\ifhmode\unskip\nobreak\fi\ifmmode\ifinner\else\hskip5 pt \fi\fi - \hbox{\hskip25 pt \hbox{\vrule width .2 pt \vbox{\hrule width 4 pt - height .2 pt \vskip 6.2 pt \hrule width 4 pt height .2 pt }\unskip\vrule - width .2 pt }\hskip 0pt }} -\centerline{\bf USING THE \AmSTeX\ SIAM STYLE FILE} -\medskip -{\eightpt\centerline{BRADLEY J. LUCIER and DOUGLAS N. ARNOLD}} -\bigskip -The \AmSTeX\ SIAM style file, amstexsiam.sty, is intended to help -authors to produce a paper that is typographically acceptable for -publication in a SIAM journal. Beginning with version 2, -amstexsiam.sty inputs amsppt.sty and then makes modifications as -necessary. Version 2 of amstexsiam.sty works with version 2.1 of -\AmSTeX\ and version 2.1a of amsppt.sty, and should work with latter -versions. This brief guide assumes familiarity with \AmSTeX\ and -amsppt, as documented in {\it The Joy of \TeX\ } by Michael Spivak. - -Most of the points introduced below are illustrated in the nonsense -paper {\it A sample paper, with a rather long title, to illustrate the -\AmSTeX\ SIAM style}. - -\heading{Publication information} When the paper has been accepted, -10 lines similar to these should be place immediately -after the \v"documentsyle" line: -\medskip -\beginverbatim -\accepted\SINUM -\firstpageno{10} -\lastpageno{12} -\issuevolume{1} -\issuenumber{2} -\issuemonth{February} -\placenumber{002} -\issueyear{1988} -\shortauthor{Bradley J. Lucier and Douglas N. Arnold} -\shorttitle{A Sample Paper} -\endverbatim -\medskip\noindent -The \v"\accepted" macro should be followed by a control sequence taken -from the following table indicating the specific journal. -\medskip -\settabs\+\indent&Acronym\indent&Title&\cr -\+& \v"\SINUM"&SIAM Journal on Numerical Analysis&\cr -\+& \v"\SIREV"&SIAM Review&\cr -\+& \v"\SIMA"&SIAM Journal on Mathematical Analysis&\cr -\+& \v"\SIMAX"&SIAM Journal on Matrix Analysis and Applications&\cr -\+& \v"\SICOMP"&SIAM Journal on Computing&\cr -\+& \v"\SISC"&SIAM Journal on Scientific Computing&\cr -\+& \v"\SIOPT"&SIAM Journal on Optimization&\cr -\+& \v"\SIAP"&SIAM Journal on Applied Mathematics&\cr -\+& \v"\SICON"&SIAM Journal on Control and Optimization&\cr -\+& \v"\SIDMA"&SIAM Journal on Discrete Mathematics&\cr -\medskip\noindent -The next lines give information for the publication data printed at the -top of the first page of the paper and for the running heads. This -information consists of the first page number of the article, the last -page number of the article, the journal name, the issue volume, the -issue number, the month of appearance, the year of appearance, the -place of the paper in the issue, the head for even pages (the -author(s)'s name(s) shortened if necessary to fit on the headline), and -the head for odd pages (the title shortened if necessary). If the -\v"\accepted" macro is not present, the publication information will be -ignored except for \v"\shortauthor" and \v"\shorttitle", which may be -used for page headers. - -\heading{Top matter} The {\it only}\/ constructions allowed between -\v"\topmatter" and \v"\endtopmatter" are, in order, \v"\title" $\dots$ \v"\endtitle", -\v"\author" $\dots$ \v"\endauthor", \v"\abstract" $\dots$ \v"\endabstract", -\v"\keywords" $\dots$ \v"\endkeywords", and -\v"\subjclass" $\dots$ \v"\endsubjclass". (For special situations, -\v"\pretitle", \v"\preauthor", \v"\preabstract", \v"\prekeywords", -\v"\presubjclass", and \v"\prepaper" can also be defined; see {\it The -Joy of \TeX\/}). - -\heading{Title} Use \v"\title" and \v"\endtitle". Type the title in -all caps. The title may have a footnote (at final publication time -there will be a footnote indicating when the paper was received). The -footnote mark should be a bold asterisk obtained with -\v"\footnote[\boldkey*]{Text of footnote.}". All math should be typed using -\v"\boldkey" and \v"\boldsymbol" to get bold italic Roman and Greek letters -and symbols; see {\it The Joy of \TeX\/}. - -\heading{Author} Use \v"\author" and \v"\endauthor". Type the author's -name in all caps. For multiple authors include the word ``and'' in -lowercase before the name of the last author. For three or more -authors follow each author's names except the last with a comma. Give -the affiliation of each author in a footnote attached to the author's -name (before the following comma, if any). (Do {\it not} use the -\v"\affil" or \v"\address" macros.) Statements acknowledging support -should be contained in the same footnote. The order of footnote -symbols in these footnotes is dagger (\dag\thinspace =\thinspace -\v"\dag"), double-dagger (\ddag\thinspace =\thinspace \v"\ddag"), -section-marker (\S\thinspace = \thinspace\v"\S"), paragraph-marker -(\P\thinspace = \thinspace\v"\P"). - -\heading{Abstract} Use \v"\abstract" and \v"\endabstract". - -\heading{Keywords} Use \v"\keywords" and \v"\endkeywords". Keywords are separated with commas but not followed by any punctuation. - -\heading{Subject classifications} Use \v"\subjclass" and -\v"\endsubjclass". Subject classifications are separated with commas -but not followed by any punctuation. - -\heading{Footnotes} Use \v"\footnote". Except for the topmatter, discussed -above, use numbered footnotes. - -\heading{Headings} Use \v"\subheading" without ending punctuation. The -argument usually begins with the section number followed by a period -and then the section name with only the first word capitalized. Very -long papers could use \v"\heading" and \v"\subheading". If -\v"\heading" is used, start heading name with a section mark -(\S\thinspace =\thinspace\v"\S") and the section number followed by a -period and the section title with the first letter of each major word -capitalized. All math should be typed using -\v"\boldkey" and \v"\boldsymbol" to get bold italic Roman and Greek letters -and symbols; see {\it The Joy of \TeX\/}. - - -\heading{Equation numbers} Use \v"\tag". - -\heading{Proclamations} Use \v"\proclaim" $\dots$ \v"\endproclaim" -for theorems, lemmas, corollaries, claims, propositions, etc. Use -\v"\demo" $\dots$ \v"\enddemo" for proofs, \v"\remark" $\dots$ \v"\endremark" -for remarks, -\v"\definition" $\dots$ \v"\enddefinition" for definitions, -\v"\example" $\dots$ \v"\endexample" for examples, and \v"\case" $\dots$ \v"\endcase" -for cases. In each construction the -opening control sequence (\v"\proclaim", \v"\demo", $\dots$ ) takes -a single argument with no closing punctuation as in \v"\proclaim{Theorem 2.3}" -or \v"\demo{Proof}". If remarks, examples, or cases are to be numbered, -you must explicitly change to roman type for the number: -\v"\remark{Remark \rom{3}}". - -\heading{Punctuation} All vertical punctuation symbols, i.e.,~), (, :, ;, -?, !, ], and [, and numbers are to be set on roman type, even if in italic -text (e.g.,~in proclaims or in the headings of demos, remarks, etc.). One -can do this with, for example, the \v"\rom" macro, as \v"{\it Assume that -\rom{(1.1)} holds.}" or \v"{\it Fermat's Last Theorem is true \rom(this is new\rom).}", which yield {\it Assume that -{\rm (1.1)} holds.} and {\it Fermat's Last Theorem is true {\rm(}this is new\/{\rm)}.} - -\heading{End-of-proof mark}The symbol signalling the end of a proof -is an open box, shown at the end of this paragraph. It is obtained -with \v"\qed". Appropriate white space will be supplied -automatically.\qed - -\heading{Lists and sublists} Use \v"\roster" $\dots$ \v"\endroster". -Rosters use default labels of the form (1), (2), etc. Subrosters are -permitted. Each subroster {\it must}\/ be enclosed in a separate pair -of braces. - -\heading{References} Enclose the reference section with \v"\Refs" -$\dots$ \v"\endRefs". References are set just as described in {\it The -Joy of \TeX.} Authors' names must be entered as first and possibly -middle initial, each followed by a period and a space, followed by the -last name. Only the first letter of the last name is capitalized. -Use \v"\by" before either \v"\ed" or \v"\eds". - -\heading{Figures and tables} There is only rudimentary support for -figures and tables in the style file. Use -\v"\topinsert" $\dots$ \v"\endinsert" or -\v"\midinsert" $\dots$ \v"\endinsert" to surround a figure, including the -caption at the end as, for example, \v"\botcaption{Fig.~1} This is a -figure caption.\endcaption". Use \v"\topinsert" $\dots$ \v"\endinsert" -or \v"\midinsert" $\dots$ \v"\endinsert"to surround the table, including -the caption at the start as, for example, \v"\topcaption{Table 1}This -line describes the table\endcaption". -Place rules above and below column headings and at the -end of the table using \v"\hbox to \hsize{\hrulefill}". - -\heading{Table of contents} No special macros are provided to set -a table of contents. You can try the macros described in {\it The Joy of -\TeX\/}. Otherwise, follow these -guidelines. Switch to eight point type (\v"\eightpoint"). -Center the word ``CONTENTS'' in caps. Capitalize only the first word -of entries. Runover lines align with the start of entries. -Place the section number flush left with one em to section title, -spaced dots from end of entry to page number, and two ems between the -dots and page number. Leave 18--20 points of vertical space, baseline -to baseline, to the text above and below. - -\bye - diff --git a/Master/texmf-dist/tex/latex/siam/numinsec.sty b/Master/texmf-dist/tex/latex/siam/numinsec.sty deleted file mode 100644 index b39729eb345..00000000000 --- a/Master/texmf-dist/tex/latex/siam/numinsec.sty +++ /dev/null @@ -1,18 +0,0 @@ -% ====================== NUMINSEC.STY ============================ % -% SIAM Style option to get numbering of equations, figures, tables within -%sections - -\@addtoreset{equation}{section} % Makes \section reset 'equation' counter. -\def\theequation{\thesection.\arabic{equation}} - -\@addtoreset{theorem}{section} -\def\thetheorem{\thesection.\@arabic\c@theorem} -\def\thelemma{\thesection.\@arabic\c@theorem} -\def\thecorollary{\thecorollary.\@arabic\c@theorem} -\def\theproposition{\theproposition.\@arabic\c@theorem} - -\@addtoreset{figure}{section} -\def\thefigure{\thesection.\@arabic\c@figure} - -\@addtoreset{table}{section} -\def\thetable{\thesection.\@arabic\c@table} diff --git a/Master/texmf-dist/tex/latex/siam/siam10.clo b/Master/texmf-dist/tex/latex/siam/siam10.clo deleted file mode 100644 index 67ce632bef5..00000000000 --- a/Master/texmf-dist/tex/latex/siam/siam10.clo +++ /dev/null @@ -1,209 +0,0 @@ -%% -%% This is file `siam10.clo', based on size10.clo -%% Revision of siam macros for use with LaTeX 2e -%% -%% By Paul Duggan for the Society for Industrial and Applied -%% Mathematics. -%% -%% October 1, 1995 -%% -%% Version 1.0 -%% -%% You are not allowed to change this file. -%% -%% You are allowed to distribute this file under the condition that -%% it is distributed together with all of the files in the siam macro -%% distribution. These are: -%% -%% siamltex.cls (main LaTeX macro for SIAM) -%% siamltex.sty (includes siamltex.cls for compatibility mode) -%% siam10.clo (this file) -%% subeqn.clo (allows equation numbners with lettered subelements) -%% siam.bst (bibliographic style file for use with BibTeX) -%% docultex.tex (documentation file) -%% lexample.tex (example file for latex macro) -%% -%% If you receive only some of these files from someone, complain! -%% -%% You are NOT ALLOWED to distribute this file alone. You are NOT -%% ALLOWED to take money for the distribution or use of either this -%% file or a changed version, except for a nominal charge for copying -%% etc. -%% \CharacterTable -%% {Upper-case \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z -%% Lower-case \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z -%% Digits \0\1\2\3\4\5\6\7\8\9 -%% Exclamation \! Double quote \" Hash (number) \# -%% Dollar \$ Percent \% Ampersand \& -%% Acute accent \' Left paren \( Right paren \) -%% Asterisk \* Plus \+ Comma \, -%% Minus \- Point \. Solidus \/ -%% Colon \: Semicolon \; Less than \< -%% Equals \= Greater than \> Question mark \? -%% Commercial at \@ Left bracket \[ Backslash \\ -%% Right bracket \] Circumflex \^ Underscore \_ -%% Grave accent \` Left brace \{ Vertical bar \| -%% Right brace \} Tilde \~} -\ProvidesFile{siam10.clo} - [1994/10/01 v1.0 - SIAM LaTeX file (size option)] -\renewcommand{\normalsize}{% - \@setfontsize\normalsize\@xpt\@xiipt - \abovedisplayskip 10\p@ \@plus2\p@ \@minus5\p@ - \abovedisplayshortskip \abovedisplayskip - \belowdisplayshortskip \belowdisplayskip - \belowdisplayskip \abovedisplayskip - \let\@listi\@listI} -\normalsize -\newcommand{\small}{% - \@setfontsize\small\@ixpt{11}% - \abovedisplayskip 8.5\p@ \@plus3\p@ \@minus4\p@ - \abovedisplayshortskip \z@ \@plus2\p@ - \belowdisplayshortskip 4\p@ \@plus2\p@ \@minus2\p@ - \def\@listi{\leftmargin\leftmargini - \topsep 4\p@ \@plus2\p@ \@minus2\p@ - \parsep 2\p@ \@plus\p@ \@minus\p@ - \itemsep \parsep}% - \belowdisplayskip \abovedisplayskip -} -\newcommand{\footnotesize}{% - \@setfontsize\footnotesize\@viiipt{9.5}% - \abovedisplayskip 6\p@ \@plus2\p@ \@minus4\p@ - \abovedisplayshortskip \abovedisplayskip - \belowdisplayshortskip \belowdisplayskip - \def\@listi{\leftmargin\leftmargini - \topsep \z@ - \parsep \z@ - \itemsep \parsep}% - \belowdisplayskip \abovedisplayskip -} -\newcommand{\scriptsize}{\@setfontsize\scriptsize\@viipt\@viiipt} -\newcommand{\tiny}{\@setfontsize\tiny\@vpt\@vipt} -\newcommand{\large}{\@setfontsize\large\@xiipt{14}} -\newcommand{\Large}{\@setfontsize\Large\@xivpt{18}} -\newcommand{\LARGE}{\@setfontsize\LARGE\@xviipt{22}} -\newcommand{\huge}{\@setfontsize\huge\@xxpt{25}} -\newcommand{\Huge}{\@setfontsize\Huge\@xxvpt{30}} -\if@twocolumn - \setlength\parindent{1em} -\else - \setlength\parindent{.25in} -\fi -\setlength\headheight{10\p@} -\setlength\headsep {.2in} -%\setlength\topskip {10\p@} -\setlength\footskip{.2in} -\if@compatibility - \setlength\maxdepth{4\p@} -\else - \setlength\maxdepth{.5\topskip} -\fi -\setlength\@maxdepth\maxdepth -\if@compatibility - \if@twocolumn - \setlength\textwidth{410\p@} - \else - \setlength\textwidth{5.125in} - \fi -\else - \if@twocolumn - \setlength\textwidth{410\p@} - \else - \setlength\textwidth{5.125in} - \fi -\fi -%\if@compatibility\else -% \@settopoint\textwidth -%\fi -\if@compatibility - \setlength\textheight{8.25in} -\else - \setlength\textheight{8.25in} -\fi -%\addtolength\textheight{\topskip} -\if@compatibility - \if@twoside - \setlength\oddsidemargin {.5in} - \setlength\evensidemargin {.5in} - \setlength\marginparwidth {1.25in} - \else - \setlength\oddsidemargin {.5in} - \setlength\evensidemargin {.5in} - \setlength\marginparwidth {1.25in} - \fi - \if@twocolumn - \setlength\oddsidemargin {30\p@} - \setlength\evensidemargin {30\p@} - \setlength\marginparwidth {48\p@} - \fi -\else - \if@twoside - \setlength\oddsidemargin {.5in} - \setlength\evensidemargin {.5in} - \setlength\marginparwidth {1.25in} - \else - \setlength\oddsidemargin {.5in} - \setlength\evensidemargin {.5in} - \setlength\marginparwidth {1.25in} - \fi - \@settopoint\oddsidemargin - \@settopoint\marginparwidth -\fi -\if@twocolumn - \setlength\marginparsep {10\p@} -\else - \setlength\marginparsep{11\p@} -\fi -\setlength\marginparpush{5\p@} -\if@compatibility - \setlength\topmargin{\z@} -\else -\setlength\topmargin {\z@} -% \@settopoint\topmargin -\fi - -\setlength\footnotesep{6.65\p@} -\skip\footins 13\p@ \@plus 4\p@ \@minus 2\p@ -\setlength\floatsep {12\p@ \@plus 2\p@ \@minus 2\p@} -\setlength\textfloatsep{20\p@ \@plus 2\p@ \@minus 4\p@} -\setlength\intextsep {12\p@ \@plus 2\p@ \@minus 2\p@} -\setlength\dblfloatsep {12\p@ \@plus 2\p@ \@minus 2\p@} -\setlength\dbltextfloatsep{20\p@ \@plus 2\p@ \@minus 4\p@} -\setlength\@fptop{0\p@ \@plus 1fil} -\setlength\@fpsep{8\p@ \@plus 2fil} -\setlength\@fpbot{0\p@ \@plus 1fil} -\setlength\@dblfptop{0\p@ \@plus 1fil} -\setlength\@dblfpsep{8\p@ \@plus 2fil} -\setlength\@dblfpbot{0\p@ \@plus 1fil} -\setlength\partopsep{\z@} -\def\@listI{\leftmargin\leftmargini - \parsep \z@ - \topsep \z@ - \itemsep \parsep} -\let\@listi\@listI -\@listi -\def\@listii {\leftmargin\leftmarginii - \labelwidth\leftmarginii - \advance\labelwidth-\labelsep - \topsep \z@ - \parsep \z@ - \itemsep \parsep} -\def\@listiii{\leftmargin\leftmarginiii - \labelwidth\leftmarginiii - \advance\labelwidth-\labelsep - \topsep \z@ - \parsep \z@ - \partopsep \z@ - \itemsep \topsep} -\def\@listiv {\leftmargin\leftmarginiv - \labelwidth\leftmarginiv - \advance\labelwidth-\labelsep} -\def\@listv {\leftmargin\leftmarginv - \labelwidth\leftmarginv - \advance\labelwidth-\labelsep} -\def\@listvi {\leftmargin\leftmarginvi - \labelwidth\leftmarginvi - \advance\labelwidth-\labelsep} -\endinput -%% -%% End of file `siam10.clo'. diff --git a/Master/texmf-dist/tex/latex/siam/siam10.sty b/Master/texmf-dist/tex/latex/siam/siam10.sty deleted file mode 100644 index 73444961e72..00000000000 --- a/Master/texmf-dist/tex/latex/siam/siam10.sty +++ /dev/null @@ -1,104 +0,0 @@ -% ====================== SIAM10.STY ============================== % -% siam10.sty 4 Sep 92, based on art10.sty 22 Dec 87 -\lineskip 1pt \normallineskip 1pt -\def\baselinestretch{1} - -\def\@normalsize{\@setsize\normalsize{12pt}\xpt\@xpt -\abovedisplayskip 10pt plus2pt minus5pt\belowdisplayskip \abovedisplayskip -\abovedisplayshortskip \abovedisplayskip -\belowdisplayshortskip \belowdisplayskip \let\@listi\@listI} -\def\small{\@setsize\small{11pt}\ixpt\@ixpt -\abovedisplayskip 8.5pt plus 3pt minus 4pt\belowdisplayskip \abovedisplayskip -\abovedisplayshortskip \abovedisplayskip\belowdisplayshortskip \belowdisplayskip -\def\@listi{\leftmargin\leftmargini \leftmargin\leftmargini \topsep \z@\parsep \z@ -\itemsep \parsep}} -\def\footnotesize{\@setsize\footnotesize{9.5pt}\viiipt\@viiipt -\abovedisplayskip 6pt plus 2pt minus 4pt\belowdisplayskip \abovedisplayskip -\abovedisplayshortskip \abovedisplayskip\belowdisplayshortskip \belowdisplayskip -\def\@listi{\leftmargin\leftmargini \topsep \z@\parsep \z@ -\itemsep \parsep}} -\def\scriptsize{\@setsize\scriptsize{8pt}\viipt\@viipt} -\def\tiny{\@setsize\tiny{6pt}\vpt\@vpt} -\def\large{\@setsize\large{14pt}\xiipt\@xiipt} -\def\Large{\@setsize\Large{18pt}\xivpt\@xivpt} -\def\LARGE{\@setsize\LARGE{22pt}\xviipt\@xviipt} -\def\huge{\@setsize\huge{25pt}\xxpt\@xxpt} -\def\Huge{\@setsize\Huge{30pt}\xxvpt\@xxvpt} -\normalsize - -\oddsidemargin .5in \evensidemargin .5in -\marginparwidth 1.25in \marginparsep .25in - \topmargin \z@ \headheight 10pt \headsep .2in \footskip .2in - -\textheight 8.25in \textwidth 5.125in \columnsep 10pt \columnseprule 0pt - -\footnotesep 6.65pt -\skip\footins 13pt plus 4pt minus 2pt -\floatsep 12pt plus 2pt minus 2pt \textfloatsep 20pt plus 2pt minus 4pt -\intextsep 12pt plus 2pt minus 2pt \@maxsep 20pt \dblfloatsep 12pt plus 2pt -minus 2pt \dbltextfloatsep 20pt plus 2pt minus 4pt \@dblmaxsep 20pt -\@fptop 0pt plus 1fil \@fpsep 8pt plus 2fil \@fpbot 0pt plus 1fil -\@dblfptop 0pt plus 1fil \@dblfpsep 8pt plus 2fil \@dblfpbot 0pt plus 1fil -\marginparpush 5pt - -\parskip 0pt plus 1pt \parindent .25in \partopsep \z@ -\@lowpenalty 51 \@medpenalty 151 \@highpenalty 301 -\@beginparpenalty -\@lowpenalty \@endparpenalty -\@lowpenalty \@itempenalty --\@lowpenalty - - -\def\part{\par \addvspace{4ex} \@afterindentfalse \secdef\@part\@spart} -\def\@part[#1]#2{\ifnum \c@secnumdepth >\m@ne \refstepcounter{part} -\addcontentsline{toc}{part}{\thepart \hspace{1em}#1}\else -\addcontentsline{toc}{part}{#1}\fi { \parindent 0pt \raggedright - \ifnum \c@secnumdepth >\m@ne \bf Part \thepart \par \nobreak \fi -\bf #2\markboth{}{}\par } \nobreak \vskip 3ex \@afterheading } -\def\@spart#1{{\parindent 0pt \raggedright - \bf - #1\par} \nobreak \vskip 3ex \@afterheading } -\def\section{\@startsection {section}{1}{.25in}{1.3ex plus .5ex minus - .2ex}{-.5em plus -.1em}{\bf}} -\def\subsection{\@startsection {subsection}{2}{.25in}{1.3ex plus .5ex minus - .2ex}{-.5em plus -.1em}{\bf}} -\def\subsubsection{\@startsection {subsubsection}{3}{.25in}{1.3ex plus .5ex minus - .2ex}{-.5em plus -.1em}{\bf}} -\def\paragraph{\@startsection {paragraph}{4}{.25in}{1.3ex plus .5ex minus - .2ex}{-.5em plus -.1em}{\it}} -\def\subparagraph{\@startsection {subparagraph}{4}{.25in}{1.3ex plus .5ex minus - .2ex}{-.5em plus -.1em}{\it}} - - -\setcounter{secnumdepth}{3} - -\def\appendix{\par - \setcounter{section}{0} - \setcounter{subsection}{0} - \def\thesection{\Alph{section}}} - - -\leftmargini 0.5in -\leftmarginii 22pt \leftmarginiii 18.7pt \leftmarginiv 17pt \leftmarginv 10pt -\leftmarginvi 10pt -\leftmargin\leftmargini -\labelsep 5pt -\labelwidth\leftmargini\advance\labelwidth-\labelsep -\def\@listI{\leftmargin\leftmargini \parsep \z@ \topsep \z@ \itemsep \parsep} -\let\@listi\@listI -\@listi -\def\@listii{\leftmargin\leftmarginii - \labelwidth\leftmarginii\advance\labelwidth-\labelsep - \topsep \z@ - \parsep \z@ - \itemsep \parsep} -\def\@listiii{\leftmargin\leftmarginiii - \labelwidth\leftmarginiii\advance\labelwidth-\labelsep - \topsep \z@ - \parsep \z@ \partopsep \z@ - \itemsep \topsep} -\def\@listiv{\leftmargin\leftmarginiv - \labelwidth\leftmarginiv\advance\labelwidth-\labelsep} -\def\@listv{\leftmargin\leftmarginv - \labelwidth\leftmarginv\advance\labelwidth-\labelsep} -\def\@listvi{\leftmargin\leftmarginvi - \labelwidth\leftmarginvi\advance\labelwidth-\labelsep} - diff --git a/Master/texmf-dist/tex/latex/siam/siam11.sty b/Master/texmf-dist/tex/latex/siam/siam11.sty deleted file mode 100644 index c74e758abd4..00000000000 --- a/Master/texmf-dist/tex/latex/siam/siam11.sty +++ /dev/null @@ -1,106 +0,0 @@ -% ====================== SIAM11.STY ============================== % -% siam11.sty 4 Sep 92, based on art11.sty 22 Dec 87 -\lineskip 1pt \normallineskip 1pt -\def\baselinestretch{1} - -\def\@normalsize{\@setsize\normalsize{13.6pt}\xipt\@xipt -\abovedisplayskip 11pt plus3pt minus6pt\belowdisplayskip \abovedisplayskip -\abovedisplayshortskip \abovedisplayskip -\belowdisplayshortskip \belowdisplayskip \let\@listi\@listI} -\def\small{\@setsize\small{12pt}\xpt\@xpt -\abovedisplayskip 10pt plus2pt minus5pt\belowdisplayskip \abovedisplayskip -\abovedisplayshortskip \abovedisplayskip\belowdisplayshortskip \belowdisplayskip -\def\@listi{\leftmargin\leftmargini \topsep \z@\parsep \z@ -\itemsep \parsep}} -\def\footnotesize{\@setsize\footnotesize{11pt}\ixpt\@ixpt -\abovedisplayskip 8pt plus 2pt minus 4pt\belowdisplayskip \abovedisplayskip -\abovedisplayshortskip \abovedisplayskip\belowdisplayshortskip \belowdisplayskip -\def\@listi{\leftmargin\leftmargini \topsep \z@\parsep \z@ -\itemsep \parsep}} -\def\scriptsize{\@setsize\scriptsize{9.5pt}\viiipt\@viiipt} -\def\tiny{\@setsize\tiny{7pt}\vipt\@vipt} -\def\large{\@setsize\large{14pt}\xiipt\@xiipt} -\def\Large{\@setsize\Large{18pt}\xivpt\@xivpt} -\def\LARGE{\@setsize\LARGE{22pt}\xviipt\@xviipt} -\def\huge{\@setsize\huge{25pt}\xxpt\@xxpt} -\def\Huge{\@setsize\Huge{30pt}\xxvpt\@xxvpt} -\normalsize - -\voffset -.4in -\oddsidemargin .3in \evensidemargin .3in -\marginparwidth 1.14in \marginparsep .25in - \topmargin \z@ \headheight 11pt \headsep .22in \footskip .22in - -\textheight 9in \textwidth 5.64in \columnsep 11pt \columnseprule 0pt - -\footnotesep 7.3pt -\skip\footins 14pt plus 4pt minus 2pt -\floatsep 12pt plus 2pt minus 2pt \textfloatsep 20pt plus 2pt minus 4pt -\intextsep 12pt plus 2pt minus 2pt \@maxsep 20pt \dblfloatsep 12pt plus 2pt -minus 2pt \dbltextfloatsep 20pt plus 2pt minus 4pt \@dblmaxsep 20pt -\@fptop 0pt plus 1fil \@fpsep 8pt plus 2fil \@fpbot 0pt plus 1fil -\@dblfptop 0pt plus 1fil \@dblfpsep 8pt plus 2fil \@dblfpbot 0pt plus 1fil -\marginparpush 5pt - -\parskip 0pt plus 1pt \parindent .275in \partopsep \z@ -\@lowpenalty 51 \@medpenalty 151 \@highpenalty 301 -\@beginparpenalty -\@lowpenalty \@endparpenalty -\@lowpenalty \@itempenalty --\@lowpenalty - - -\def\part{\par \addvspace{4ex} \@afterindentfalse \secdef\@part\@spart} -\def\@part[#1]#2{\ifnum \c@secnumdepth >\m@ne \refstepcounter{part} -\addcontentsline{toc}{part}{\thepart \hspace{1em}#1}\else -\addcontentsline{toc}{part}{#1}\fi { \parindent 0pt \raggedright - \ifnum \c@secnumdepth >\m@ne \bf Part \thepart \par \nobreak \fi -\bf #2\markboth{}{}\par } \nobreak \vskip 3ex \@afterheading } -\def\@spart#1{{\parindent 0pt \raggedright - \bf - #1\par} \nobreak \vskip 3ex \@afterheading } -\def\section{\@startsection {section}{1}{.275in}{1.4ex plus .5ex minus - .2ex}{-.55em plus -.1em}{\bf}} -\def\subsection{\@startsection {subsection}{2}{.275in}{1.4ex plus .5ex minus - .2ex}{-.55em plus -.1em}{\bf}} -\def\subsubsection{\@startsection {subsubsection}{3}{.275in}{1.4ex plus .5ex minus - .2ex}{-.55em plus -.1em}{\bf}} -\def\paragraph{\@startsection {paragraph}{4}{.275in}{1.4ex plus .5ex minus - .2ex}{-.55em plus -.1em}{\it}} -\def\subparagraph{\@startsection {subparagraph}{4}{.275in}{1.4ex plus .5ex minus - .2ex}{-.55em plus -.1em}{\it}} - - -\setcounter{secnumdepth}{3} - -\def\appendix{\par - \setcounter{section}{0} - \setcounter{subsection}{0} - \def\thesection{\Alph{section}}} - - -\leftmargini .55in -\leftmarginii 2.2em \leftmarginiii 1.87em \leftmarginiv 1.7em \leftmarginv 1em -\leftmarginvi 1em -\leftmargin\leftmargini -\labelsep .5em -\labelwidth\leftmargini\advance\labelwidth-\labelsep -\def\@listI{\leftmargin\leftmargini \parsep \z@ \topsep \z@ \itemsep \parsep} -\let\@listi\@listI -\@listi -\def\@listii{\leftmargin\leftmarginii - \labelwidth\leftmarginii\advance\labelwidth-\labelsep - \topsep \z@ - \parsep \z@ - \itemsep \parsep} -\def\@listiii{\leftmargin\leftmarginiii - \labelwidth\leftmarginiii\advance\labelwidth-\labelsep - \topsep \z@ - \parsep \z@ \partopsep \z@ - \itemsep \topsep} -\def\@listiv{\leftmargin\leftmarginiv - \labelwidth\leftmarginiv\advance\labelwidth-\labelsep} -\def\@listv{\leftmargin\leftmarginv - \labelwidth\leftmarginv\advance\labelwidth-\labelsep} -\def\@listvi{\leftmargin\leftmarginvi - \labelwidth\leftmarginvi\advance\labelwidth-\labelsep} - - diff --git a/Master/texmf-dist/tex/latex/siam/siamltex.cls b/Master/texmf-dist/tex/latex/siam/siamltex.cls deleted file mode 100644 index dad7e12b390..00000000000 --- a/Master/texmf-dist/tex/latex/siam/siamltex.cls +++ /dev/null @@ -1,628 +0,0 @@ -%% -%% This is file `siamltex.cls', based on article.cls -%% Revision of siam macros for use with LaTeX 2e -%% -%% By Paul Duggan for the Society for Industrial and Applied -%% Mathematics. -%% -%% October 1, 1995 -%% -%% Version 1.0 -%% -%% You are not allowed to change this file. -%% -%% You are allowed to distribute this file under the condition that -%% it is distributed together with all of the files in the siam macro -%% distribution. These are: -%% -%% siamltex.cls (this file) -%% siamltex.sty (includes siamltex.cls for compatibility mode) -%% siam10.clo (size option for 10pt papers) -%% subeqn.clo (allows equation numbners with lettered subelements) -%% siam.bst (bibliographic style file for BibTeX) -%% docultex.tex (documentation file) -%% lexample.tex (example file for latex macro) -%% -%% If you receive only some of these files from someone, complain! -%% -%% You are NOT ALLOWED to distribute this file alone. You are NOT -%% ALLOWED to take money for the distribution or use of either this -%% file or a changed version, except for a nominal charge for copying -%% etc. -%% \CharacterTable -%% {Upper-case \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z -%% Lower-case \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z -%% Digits \0\1\2\3\4\5\6\7\8\9 -%% Exclamation \! Double quote \" Hash (number) \# -%% Dollar \$ Percent \% Ampersand \& -%% Acute accent \' Left paren \( Right paren \) -%% Asterisk \* Plus \+ Comma \, -%% Minus \- Point \. Solidus \/ -%% Colon \: Semicolon \; Less than \< -%% Equals \= Greater than \> Question mark \? -%% Commercial at \@ Left bracket \[ Backslash \\ -%% Right bracket \] Circumflex \^ Underscore \_ -%% Grave accent \` Left brace \{ Vertical bar \| -%% Right brace \} Tilde \~} -\NeedsTeXFormat{LaTeX2e} -\ProvidesClass{siamltex} - [1995/10/01 v1.0 LaTeX document class] -\newcommand\@ptsize{} -\newif\if@restonecol -\newif\if@titlepage -\@titlepagefalse -%\newif\if@openbib -%\@openbibfalse -\DeclareOption{a4paper} - {\setlength\paperheight {297mm}% - \setlength\paperwidth {210mm}} -\DeclareOption{a5paper} - {\setlength\paperheight {210mm}% - \setlength\paperwidth {148mm}} -\DeclareOption{b5paper} - {\setlength\paperheight {250mm}% - \setlength\paperwidth {176mm}} -\DeclareOption{letterpaper} - {\setlength\paperheight {11in}% - \setlength\paperwidth {8.5in}} -\DeclareOption{legalpaper} - {\setlength\paperheight {14in}% - \setlength\paperwidth {8.5in}} -\DeclareOption{executivepaper} - {\setlength\paperheight {10.5in}% - \setlength\paperwidth {7.25in}} -\DeclareOption{landscape} - {\setlength\@tempdima {\paperheight}% - \setlength\paperheight {\paperwidth}% - \setlength\paperwidth {\@tempdima}} -\DeclareOption{10pt}{\renewcommand\@ptsize{0}} -\DeclareOption{11pt}{\renewcommand\@ptsize{1}} -\DeclareOption{12pt}{\renewcommand\@ptsize{2}} -\DeclareOption{twoside}{\@twosidetrue \@mparswitchtrue} -\DeclareOption{draft}{\setlength\overfullrule{5pt}} -\DeclareOption{final}{\setlength\overfullrule{0pt}} -\DeclareOption{notitlepage}{\@titlepagefalse} -\DeclareOption{onecolumn}{\@twocolumnfalse} -\DeclareOption{twocolumn}{\@twocolumntrue} -\DeclareOption{leqno}{\input{leqno.clo}} -\DeclareOption{subeqn}{\input{subeqn.clo}} -%\DeclareOption{openbib}{\@openbibtrue} -\ExecuteOptions{letterpaper,10pt,twoside,onecolumn,leqno,draft,notitlepage} -\ProcessOptions -\input{siam1\@ptsize.clo} -\setlength\lineskip{1\p@} -\setlength\normallineskip{1\p@} -\renewcommand\baselinestretch{} -\setlength\parskip{0\p@ \@plus \p@} -\@lowpenalty 51 -\@medpenalty 151 -\@highpenalty 301 -\setcounter{topnumber}{2} -\renewcommand\topfraction{.9} -\setcounter{bottomnumber}{1} -\renewcommand\bottomfraction{.1} -\setcounter{totalnumber}{3} -\renewcommand\textfraction{.1} -\renewcommand\floatpagefraction{.91} -\setcounter{dbltopnumber}{2} -\renewcommand\dbltopfraction{.7} -\renewcommand\dblfloatpagefraction{.5} -\renewcommand{\ps@plain}{\let\@mkboth\@gobbletwo% - \renewcommand{\@oddhead}{}% - \renewcommand{\@evenhead}{}% - \renewcommand{\@evenfoot}{\hfil\footnotesize\textrm{\thepage}\hfil}% - \renewcommand{\@oddfoot}{\@evenfoot}} - - \def\ps@headings{% - \let\@oddfoot\@empty\let\@evenfoot\@empty - \def\@evenhead{\rlap{\thepage}\hfil\upshape\footnotesize\leftmark\hfil}% %! - \def\@oddhead{\hbox{}\hfil{\upshape\footnotesize\rightmark}\hfil\llap{\thepage}}% %! - \let\@mkboth\markboth - \def\sectionmark##1{% - \markboth {\uppercase{\ifnum \c@secnumdepth >\z@ - \thesection.\hskip 1em\relax\fi - ##1}}{}}% - \def\subsectionmark##1{% - \markright {\ifnum \c@secnumdepth >\@ne - \thesubsection\hskip 1em\relax \fi - ##1}}} - -\def\ps@myheadings{% - \let\@oddfoot\@empty\let\@evenfoot\@empty - \def\@evenhead{\rlap{\thepage}\hfil\upshape\footnotesize\leftmark\hfil}% %! - \def\@oddhead{\hbox{}\hfil{\upshape\footnotesize\rightmark}\hfil\llap{\thepage}}% %! - \let\@mkboth\@gobbletwo - \let\sectionmark\@gobble - \let\subsectionmark\@gobble - } - - -\newcommand\maketitle{\par - \begingroup - \renewcommand{\thefootnote}{\fnsymbol{footnote}}% - \def\@makefnmark{\hbox to\z@{$\m@th^{\@thefnmark}$\hss}}% - \long\def\@makefntext##1{\parindent 1em\noindent - \hbox to1.8em{\hss$\m@th^{\@thefnmark}$}##1}% - \if@twocolumn - \ifnum \col@number=\@ne - \@maketitle - \else - \twocolumn[\@maketitle]% - \fi - \else - \global\@topnum\z@ % Prevents figures from going at top of page. - \@maketitle - \fi - \thispagestyle{plain}\@thanks - \endgroup - \setcounter{footnote}{0}% - \let\maketitle\relax\let\@maketitle\relax - \gdef\@thanks{}\gdef\@author{}\gdef\@title{}\let\thanks\relax} -\def\@maketitle{% - \null - \begin{center}% - {\bfseries\@ucnothanks\@title\par}% - \vskip .075in% - {\footnotesize - \spaceskip=1.5\fontdimen2\the\font - \def\and{\ \scriptsize AND } - \@tempswafalse\expandafter\@doauth\@author\and\relax}% - \end{center}% - \par - \vskip .11in} -\def\@ucnothanks#1{\expandafter\@ucnt#1\thanks\relax} -\def\@ucnt#1\thanks{\uppercase{#1}\futurelet\@tempa\@ucnta} -\def\@ucnta{\ifx\@tempa\relax\else\@ucntb\fi} -\def\@ucntb#1\thanks\relax{\thanks{#1}} -\def\@doauth#1\and{\let\@nextdoa=\@doauth - \def\@tempc{\@ucnothanks{#1}} - \futurelet\@tempa\@doautha} -\def\@doautha{\ifx\@tempa\relax - \if@tempswa {\and}\fi - \let\@nextdoa=\relax - \else - \if@tempswa \gdef\and{,\ \scriptsize AND }, \fi - \fi - \@tempc\unskip\@tempswatrue\@nextdoa} -\let\and=\relax - - - -\setcounter{secnumdepth}{3} -\newcounter {section} -\newcounter {subsection}[section] -\newcounter {subsubsection}[subsection] -\newcounter {paragraph}[subsubsection] -\newcounter {subparagraph}[paragraph] -\renewcommand\thesection {\arabic{section}} -\renewcommand\thesubsection {\thesection.\arabic{subsection}} -\renewcommand\thesubsubsection {\thesubsection.\arabic{subsubsection}} -\renewcommand\theparagraph {\thesubsubsection.\arabic{paragraph}} -\renewcommand\thesubparagraph {\theparagraph.\arabic{subparagraph}} - - -\def\@sect#1#2#3#4#5#6[#7]#8{\ifnum #2>\c@secnumdepth - \def\@svsec{}\else - \refstepcounter{#1}\edef\@svsec{\csname the#1\endcsname.\hskip .5em }\fi - \@tempskipa #5\relax - \ifdim \@tempskipa>\z@ - \begingroup #6\relax - \@hangfrom{\hskip #3\relax\@svsec}{\interlinepenalty \@M #8\par} - \endgroup - \csname #1mark\endcsname{#7}\addcontentsline - {toc}{#1}{\ifnum #2>\c@secnumdepth \else - \protect\numberline{\csname the#1\endcsname}\fi - #7}\else - \def\@svsechd{#6\hskip #3\@svsec #8.\csname #1mark\endcsname - {#7}\addcontentsline - {toc}{#1}{\ifnum #2>\c@secnumdepth \else - \protect\numberline{\csname the#1\endcsname}\fi - #7}}\fi - \@xsect{#5}} -\def\@ssect#1#2#3#4#5{\@tempskipa #3\relax - \ifdim \@tempskipa>\z@ - \begingroup #4\@hangfrom{\hskip #1}{\interlinepenalty \@M -#5.\par}\endgroup - \else \def\@svsechd{#4\hskip #1\relax #5.}\fi - \@xsect{#3}} - - -\newcommand\section{\@startsection{section}{1}{.25in}% - {1.3ex \@plus .5ex \@minus .2ex}% - {-.5em \@plus -.1em}% - {\reset@font\normalsize\bfseries}} -\newcommand\subsection{\@startsection{subsection}{2}{.25in}% - {1.3ex\@plus .5ex \@minus .2ex}% - {-.5em \@plus -.1em}% - {\reset@font\normalsize\bfseries}} -\newcommand\subsubsection{\@startsection{subsubsection}{3}{.25in}% - {1.3ex\@plus .5ex \@minus .2ex}% - {-.5em \@plus -.1em}% - {\reset@font\normalsize\bfseries}} -\newcommand\paragraph{\@startsection{paragraph}{4}{.25in}% - {\parskip}% - {-.5em plus -.1em}% - {\reset@font\normalsize\itshape}} -\newcommand\subparagraph{\@startsection{subparagraph}{5}{\parindent}% - {\parskip}% - {-.5em plus -.1em}% - {\reset@font\normalsize\itshape}} -\if@twocolumn - \setlength\leftmargini {2em} -\else - \setlength\leftmargini {0.5in} -\fi -\setlength\leftmarginii {22pt} -\setlength\leftmarginiii {18.7pt} -\setlength\leftmarginiv {17pt} -\if@twocolumn - \setlength\leftmarginv {.5em} - \setlength\leftmarginvi {.5em} -\else - \setlength\leftmarginv {10pt} - \setlength\leftmarginvi {10pt} -\fi -\setlength \leftmargin{\leftmargini} -\setlength \labelsep {.5em} -\setlength \labelwidth{\leftmargini} -\addtolength\labelwidth{-\labelsep} -\@beginparpenalty -\@lowpenalty -\@endparpenalty -\@lowpenalty -\@itempenalty -\@lowpenalty -\renewcommand\theenumi{\arabic{enumi}} -\renewcommand\theenumii{\alph{enumii}} -\renewcommand\theenumiii{\roman{enumiii}} -\renewcommand\theenumiv{\Alph{enumiv}} -\newcommand\labelenumi{\theenumi.} -\newcommand\labelenumii{(\theenumii)} -\newcommand\labelenumiii{\theenumiii.} -\newcommand\labelenumiv{\theenumiv.} -\renewcommand\p@enumii{\theenumi} -\renewcommand\p@enumiii{\theenumi\theenumii} -\renewcommand\p@enumiv{\p@enumiii\theenumiii} -\newcommand\labelitemi{$\m@th\bullet$} -\newcommand\labelitemii{\normalfont\bfseries --} -\newcommand\labelitemiii{$\m@th\ast$} -\newcommand\labelitemiv{$\m@th\cdot$} -\newenvironment{description} - {\list{}{\labelwidth\z@ \itemindent-\leftmargin - \let\makelabel\descriptionlabel}} - {\endlist} -\newcommand\descriptionlabel[1]{\hspace\labelsep - \normalfont\bfseries #1} -\newcounter{rmnum} -\newenvironment{romannum} - {\begin{list}{{\rm (\roman{rmnum})}}{\usecounter{rmnum} - \setlength{\leftmargin}{0pt} - \setlength{\itemindent}{42pt}}}{\end{list}} -\newcounter{muni} -\newenvironment{remunerate} - {\begin{list}{{\rm \arabic{muni}.}}{\usecounter{muni} - \setlength{\leftmargin}{0pt} - \setlength{\itemindent}{38pt}}}{\end{list}} - -\newenvironment{@abssec}[1]{% - \if@twocolumn - \section*{#1}% - \else - \vspace{.05in}\footnotesize - \parindent .2in - {\bfseries #1. }\ignorespaces - \fi} - {\if@twocolumn\else\par\vspace{.1in}\fi} - -\newenvironment{abstract}{\begin{@abssec}{\abstractname}}{\end{@abssec}} -\newenvironment{keywords}{\begin{@abssec}{\keywordsname}}{\end{@abssec}} -\newenvironment{AMS}{\begin{@abssec}{\AMSname}}{\end{@abssec}} -\newenvironment{AM}{\begin{@abssec}{\AMname}}{\end{@abssec}} - - -\newenvironment{verse} - {\let\\=\@centercr - \list{}{\itemsep \z@ - \itemindent -1.5em% - \listparindent\itemindent - \rightmargin \leftmargin - \advance\leftmargin 1.5em}% - \item[]} - {\endlist} -\newenvironment{quotation} - {\list{}{\listparindent 1.5em% - \itemindent \listparindent - \rightmargin \leftmargin - \parsep \z@ \@plus\p@}% - \item[]} - {\endlist} -\newenvironment{quote} - {\list{}{\rightmargin\leftmargin}% - \item[]} - {\endlist} -\def\@begintheorem#1#2{\par\bgroup{\scshape #1\ #2. }\it\ignorespaces} -\def\@opargbegintheorem#1#2#3{\par\bgroup% - {\scshape #1\ #2\ ({\upshape #3}). }\it\ignorespaces} -\def\@endtheorem{\egroup} -\def\proof{\par{\it Proof}. \ignorespaces} - -\def\endproof{\vbox{\hrule height0.6pt\hbox{% - \vrule height1.3ex width0.6pt\hskip0.8ex - \vrule width0.6pt}\hrule height0.6pt - }} - -\newtheorem{theorem}{Theorem}[section] -\newtheorem{lemma}[theorem]{Lemma} -\newtheorem{corollary}[theorem]{Corollary} -\newtheorem{proposition}[theorem]{Proposition} -\newtheorem{definition}[theorem]{Definition} - - - -% FROM FIXUP.STY -% We now redefine the eqnarray environment to correct the space around -% the operator. Any changes to the definition in LaTeX itself -% will cause the `Warning: unable...' -% message to appear. If this happens it will be necessary to update the -% definition of \@tempb below and incorperate the changes into -% the new definitions of \eqnarray. - - -% This is the current definition of \eqnarray for the fleqn document style -% latex.ltx - -\def\@tempb{% - \stepcounter{equation}% - \def\@currentlabel{\p@equation\theequation}% - \global\@eqnswtrue - \m@th - \global\@eqcnt\z@ - \tabskip\@centering - \let\\\@eqncr - $$\everycr{}\halign to\displaywidth\bgroup - \hskip\@centering$\displaystyle\tabskip\z@skip{##}$\@eqnsel - &\global\@eqcnt\@ne\hskip \tw@\arraycolsep \hfil${##}$\hfil - &\global\@eqcnt\tw@ \hskip \tw@\arraycolsep - $\displaystyle{##}$\hfil\tabskip\@centering - &\global\@eqcnt\thr@@ \hb@xt@\z@\bgroup\hss##\egroup - \tabskip\z@skip - \cr -} -\ifx\eqnarray\@tempb % Try the default eqnarray environment - \def\eqnarray{% - \stepcounter{equation}% - \def\@currentlabel{\p@equation\theequation}% - \global\@eqnswtrue - \m@th - \global\@eqcnt\z@ - \tabskip\@centering - \let\\\@eqncr - $$\everycr{}\halign to\displaywidth\bgroup - \hskip\@centering$\displaystyle\tabskip\z@skip{##}$\@eqnsel - &\global\@eqcnt\@ne \hfil$\displaystyle{{}##{}}$\hfil - &\global\@eqcnt\tw@ $\displaystyle{##}$\hfil\tabskip\@centering - &\global\@eqcnt\thr@@ \hb@xt@\z@\bgroup\hss##\egroup - \tabskip\z@skip - \cr -} -\else \typeout{Warning: Unable to fix unknown version of \string\eqnarray.} -\fi - -\def\@tempb{} - - -%% New Mathops. - -\newcommand\const{\mathop{\operator@font const}\nolimits} -\newcommand\diag{\mathop{\operator@font diag}\nolimits} -\newcommand\grad{\mathop{\operator@font grad}\nolimits} -\newcommand\Range{\mathop{\operator@font Range}\nolimits} -\newcommand\rank{\mathop{\operator@font rank}\nolimits} -\newcommand\supp{\mathop{\operator@font supp}\nolimits} - -\newcommand\appendix{% -\renewcommand{\section}{% -\secdef\append\sappend}% - \setcounter{section}{0}% - \setcounter{subsection}{0}% - \renewcommand\thesection{\Alph{section}}} - -\newcommand\Appendix{% -\renewcommand{\section}{% -\secdef\Append\sAppend}% - \setcounter{section}{0}% - \setcounter{subsection}{0}% - \renewcommand\thesection{\Alph{section}}} - -\newcommand\append[2][?]{% -\refstepcounter{section}% -{\vskip 1.3ex \@plus .5ex \@minus .2ex -\reset@font\normalsize\bfseries\appendixname\ \thesection. #2.}} - -\newcommand\sappend[1]{% -\refstepcounter{section} -{\vskip 1.3ex \@plus .5ex \@minus .2ex -\reset@font\normalsize\bfseries\appendixname\ \thesection.}} - -\newcommand\Append[2][?]{% -\refstepcounter{section}% -{\vskip 1.3ex \@plus .5ex \@minus .2ex -\reset@font\normalsize\bfseries\appendixname. #2.}} - -\newcommand\sAppend[1]{% -\refstepcounter{section} -{\vskip 1.3ex \@plus .5ex \@minus .2ex -\reset@font\normalsize\bfseries\appendixname.}} - -\setlength\arraycolsep{5\p@} -\setlength\tabcolsep{6\p@} -\setlength\arrayrulewidth{.4\p@} -\setlength\doublerulesep{2\p@} -\setlength\tabbingsep{\labelsep} -\skip\@mpfootins = \skip\footins -\setlength\fboxsep{3\p@} -\setlength\fboxrule{.4\p@} - - -\newcounter{figure} -\renewcommand\thefigure{\@arabic\c@figure} -\def\fps@figure{tp} -\def\ftype@figure{1} -\def\ext@figure{lof} -\def\fnum@figure{\figurename~\thefigure} -\newenvironment{figure} - {\@float{figure}} - {\end@float} -\newenvironment{figure*} - {\@dblfloat{figure}} - {\end@dblfloat} -\newcounter{table} -\renewcommand{\thetable}{\@arabic\c@table} -\def\fps@table{tp} -\def\ftype@table{2} -\def\ext@table{lot} -\def\fnum@table{\tablename~\thetable} -\newenvironment{table} - {\@float{table}} - {\end@float} -\newenvironment{table*} - {\@dblfloat{table}} - {\end@dblfloat} -\newlength\abovecaptionskip -\newlength\belowcaptionskip -\setlength\abovecaptionskip{10\p@} -\setlength\belowcaptionskip{10\p@} -\def\@figtxt{figure} -\long\def\@makecaption#1#2{% - \footnotesize - \setlength{\parindent}{1.5pc} - \ifx\@captype\@figtxt - \vskip\abovecaptionskip - \setbox\@tempboxa\hbox{{\normalfont\scshape #1}. {\normalfont\itshape #2}}% - \ifdim \wd\@tempboxa >\hsize - {\normalfont\scshape #1}. {\normalfont\itshape #2}\par - \else - \global\@minipagefalse - \hb@xt@\hsize{\hfil\box\@tempboxa\hfil}% - \fi - \else - \hbox to\hsize{\hfil{\normalfont\scshape #1}\hfil}% - \setbox\@tempboxa\hbox{{\normalfont\itshape #2}}% - \ifdim \wd\@tempboxa >\hsize - {\normalfont\itshape #2}\par - \else - \global\@minipagefalse - \hb@xt@\hsize{\hfil\box\@tempboxa\hfil}% - \fi - \vskip\belowcaptionskip - \fi} -\DeclareOldFontCommand{\rm}{\normalfont\rmfamily}{\mathrm} -\DeclareOldFontCommand{\sf}{\normalfont\sffamily}{\mathsf} -\DeclareOldFontCommand{\tt}{\normalfont\ttfamily}{\mathtt} -\DeclareOldFontCommand{\bf}{\normalfont\bfseries}{\mathbf} -\DeclareOldFontCommand{\it}{\normalfont\itshape}{\mathit} -\DeclareOldFontCommand{\sl}{\normalfont\slshape}{\@nomath\sl} -\DeclareOldFontCommand{\sc}{\normalfont\scshape}{\@nomath\sc} -\DeclareRobustCommand*\cal{\@fontswitch{\relax}{\mathcal}} -\DeclareRobustCommand*\mit{\@fontswitch{\relax}{\mathnormal}} -\newcommand\@pnumwidth{1.55em} -\newcommand\@tocrmarg {2.55em} -\newcommand\@dotsep{4.5} - -\newdimen\bibindent -\bibindent=16pt -\newenvironment{thebibliography}[1] - {\par\addvspace{.25in} - \begin{center} - \footnotesize\uppercase\expandafter{\refname} - \end{center} - \@mkboth{\uppercase\expandafter{\refname}}{\uppercase\expandafter{\refname}} - \addvspace{.15in}\nopagebreak% - \list{\@biblabel{\arabic{enumi}}}% - {\settowidth\labelwidth{\@biblabel{#1}}% - \leftmargin\labelwidth - \advance\leftmargin\labelsep -% \if@openbib - \advance\leftmargin\bibindent - \itemindent -\bibindent - \listparindent \itemindent - \parsep \z@ -% \fi - \usecounter{enumi}% - \let\p@enumi\@empty - \renewcommand\theenumi{\arabic{enumi}}}% -% \if@openbib -% \renewcommand\newblock{\par} -% \else - \renewcommand\newblock{\hskip .11em \@plus.33em \@minus.07em}% -% \fi - \sloppy\clubpenalty4000\widowpenalty4000% - \sfcode`\.=\@m\relax\footnotesize} - {\def\@noitemerr - {\@latex@warning{Empty `thebibliography' environment}}% - \endlist} -\newcommand\newblock{} -\newenvironment{theindex} - {\if@twocolumn - \@restonecolfalse - \else - \@restonecoltrue - \fi - \columnseprule \z@ - \columnsep 35\p@ - \twocolumn[\section*{\indexname}]% - \@mkboth{\uppercase{\indexname}}% - {\uppercase{\indexname}}% - \thispagestyle{plain}\parindent\z@ - \parskip\z@ \@plus .3\p@\relax - \let\item\@idxitem} - {\if@restonecol\onecolumn\else\clearpage\fi} -\newcommand\@idxitem {\par\hangindent 40\p@} -\newcommand\subitem {\par\hangindent 40\p@ \hspace*{20\p@}} -\newcommand\subsubitem{\par\hangindent 40\p@ \hspace*{30\p@}} -\newcommand\indexspace{\par \vskip 10\p@ \@plus5\p@ \@minus3\p@\relax} -\renewcommand\footnoterule{% - \kern-3\p@ - \hrule width .5in - \kern 2.6\p@} -\long\def\@makefntext#1{% - \parindent .25in% - \noindent - \hbox to .25in{\hss\@makefnmark}#1} -\newcommand\contentsname{Contents} -\newcommand\listfigurename{List of Figures} -\newcommand\listtablename{List of Tables} -\newcommand\refname{References} -\newcommand\indexname{Index} -\newcommand\figurename{Fig.} -\newcommand\tablename{Table} -\newcommand\partname{Part} -\newcommand\appendixname{Appendix} -\newcommand\abstractname{Abstract} -\newcommand\keywordsname{Key words} -\newcommand\AMSname{AMS subject classifications} -\newcommand\AMname{AMS subject classification} -\newcommand\today{\ifcase\month\or - January\or February\or March\or April\or May\or June\or - July\or August\or September\or October\or November\or December\fi - \space\number\day, \number\year} -\newcommand\sameauthor{\leavevmode\vrule height 2pt depth -1.6pt width 23pt} -\setlength\columnsep{10\p@} -\setlength\columnseprule{0\p@} -\pagestyle{plain} -\pagenumbering{arabic} % Arabic page numbers - -\if@compatibility% -\else - \@addtoreset{equation}{section} % Makes \section reset 'equation' counter. - \renewcommand{\theequation}{\thesection.\arabic{equation}} -% - \@addtoreset{figure}{section} - \renewcommand{\thefigure}{\thesection.\@arabic\c@figure} -% - \@addtoreset{table}{section} - \renewcommand{\thetable}{\thesection.\@arabic\c@table} -\fi - -\onecolumn -\endinput -%% -%% End of file `siamltex.cls'. -
\ No newline at end of file diff --git a/Master/texmf-dist/tex/latex/siam/siamltex.sty b/Master/texmf-dist/tex/latex/siam/siamltex.sty deleted file mode 100644 index b36ee43e89a..00000000000 --- a/Master/texmf-dist/tex/latex/siam/siamltex.sty +++ /dev/null @@ -1,52 +0,0 @@ -%% -%% This is file `siamltex.cls', based on article.cls -%% Revision of siam macros for use with LaTeX 2e -%% -%% By Paul Duggan for the Society for Industrial and Applied -%% Mathematics. -%% -%% December 1, 1995 -%% -%% Version 1.0 -%% -%% You are not allowed to change this file. -%% -%% You are allowed to distribute this file under the condition that -%% it is distributed together with all of the files in the siam macro -%% distribution. These are: -%% -%% siamltex.cls (main macro) -%% siamltex.sty (this file) -%% siam10.clo (size option for 10pt papers) -%% subeqn.clo (allows equation numbners with lettered subelements) -%% siam.bst (bibliographic style file for BibTeX) -%% docultex.tex (documentation file) -%% lexample.tex (example file for latex macro) -%% -%% If you receive only some of these files from someone, complain! -%% -%% You are NOT ALLOWED to distribute this file alone. You are NOT -%% ALLOWED to take money for the distribution or use of either this -%% file or a changed version, except for a nominal charge for copying -%% etc. -%% \CharacterTable -%% {Upper-case \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z -%% Lower-case \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z -%% Digits \0\1\2\3\4\5\6\7\8\9 -%% Exclamation \! Double quote \" Hash (number) \# -%% Dollar \$ Percent \% Ampersand \& -%% Acute accent \' Left paren \( Right paren \) -%% Asterisk \* Plus \+ Comma \, -%% Minus \- Point \. Solidus \/ -%% Colon \: Semicolon \; Less than \< -%% Equals \= Greater than \> Question mark \? -%% Commercial at \@ Left bracket \[ Backslash \\ -%% Right bracket \] Circumflex \^ Underscore \_ -%% Grave accent \` Left brace \{ Vertical bar \| -%% Right brace \} Tilde \~} -\NeedsTeXFormat{LaTeX2e} -\@obsoletefile{siamltex.cls}{siamltex.sty} -\LoadClass{siamxtex} -\endinput -%% -%% End of file `siamltex.sty'. diff --git a/Master/texmf-dist/tex/latex/siam/subeqn.clo b/Master/texmf-dist/tex/latex/siam/subeqn.clo deleted file mode 100644 index e1fadf41319..00000000000 --- a/Master/texmf-dist/tex/latex/siam/subeqn.clo +++ /dev/null @@ -1,56 +0,0 @@ -% subeqn.sty -% ---------------------------------------------------------------------- -% This LaTeX environment is for -% printing subequations. To use this environment, include in the -% \documentstyle header a command to load in the .sty file containing this -% macro. For example: -% \documentstyle[subeqn]{article} -% if you have the macro in a file subeqn.sty. The environment seems pretty -% well documented in the comments. -% -% Modified : June 8, 1989. You can now reference either individual -% equations in the subequations environment, or all of -% them. If you use a \label command immediately after the -% \begin{subequations} command, then a reference to that -% label will generate a reference to the equation number -% without the alphabetic extension. -% -% Modified : 16 - january - 1989 by Johannes Braams ( BRAAMS@HLSDNL5) -% Added \global\@ignoretrue in the definition of -% \endsubequations in order to prevent a spurious space -% at the beginning of the next text-line. Also added %'s -% at the end of each command-line for the same reasons. -% -%%%---------------------------------------------------------------- -%%% File: subeqn.sty -%%% The subequations environment %%% -% -% Within the subequations environment, the only change is that -% equations are labeled differently. The number stays the same, -% and lower case letters are appended. For example, if after doing -% three equations, numbered 1, 2, and 3, you start a subequations -% environmment and do three more equations, they will be numbered -% 4a, 4b, and 4c. After you end the subequations environment, the -% next equation will be numbered 5. -% -% Both text and equations can be put inside the subequations environment. -% -% If you make any improvements, I'd like to hear about them. -% -% -\newtoks\@stequation - -\def\subequations{\refstepcounter{equation}% -\edef\@savedequation{\the\c@equation}% -\@stequation=\expandafter{\theequation}% %only want \theequation -\edef\@savedtheequation{\the\@stequation}% %expanded once -\edef\oldtheequation{\theequation}% -\setcounter{equation}{0}% -\def\theequation{\oldtheequation\alph{equation}}}% - -\def\endsubequations{% -\setcounter{equation}{\@savedequation}% -\@stequation=\expandafter{\@savedtheequation}% -\edef\theequation{\the\@stequation}\global\@ignoretrue} -%%%---------------------------- -
\ No newline at end of file diff --git a/Master/texmf-dist/tex/plain/siam/docuptex.tex b/Master/texmf-dist/tex/plain/siam/docuptex.tex deleted file mode 100644 index 2f673f9b7bf..00000000000 --- a/Master/texmf-dist/tex/plain/siam/docuptex.tex +++ /dev/null @@ -1,456 +0,0 @@ -%% -%% SIAM Plain TeX macro documentation. -%% Paul Duggan -%% 9-15-94 - -\input siamptex.sty - -% The definitions are to provide a verbatim text environment - -\def\uncatcodespecials{\def\do##1{\catcode`##1=12 }\dospecials} -\def\setupverbatim{\tt% - \def\par{\leavevmode\endgraf}% - \obeylines\uncatcodespecials\obeyspaces} -{\obeyspaces\global\let =\ } -\def\doverbatim#1{\def\next##1#1{##1\endgroup}\next} -\def\verbatim{\begingroup\setupverbatim\doverbatim} - - -\overfullrule=0pt - -\topmatter -\vol{1} -\no{1, pp.~000--000} -\SIMAC -\date{October 1994} -\copyyear{1994} -\code{000} - -\title Using SIAM's \TeX\ Macros\endtitle - -\shorttitle{USING SIAM'S \TeX\ MACROS} - -\recdate{*}{August 9, 1994. -This work was supported by the Society for Industrial -and Applied Mathematics} - -\author Paul Duggan\fnmark{$^{\dag}$}\endauthor - -\address{$^{\dag}$}{Society for Industrial and Applied Mathematics, -Philadelphia, Pennsylvania ({\tt duggan@siam.org}). Questions, comments, -or corrections to this document may be directed to that e-mail address} - -\abstract{Documentation is given for use of the SIAM \TeX\ macros. -Instructions and suggestions for compliance with SIAM style -standards are also included.} -\subjclass\endsubjclass -\keywords\endkeywords - - -\endtopmatter - - -\heading{1}{Introduction} -This file is documentation for the SIAM \TeX\ macros and provides -instruction for submission of files formatted in \TeX. - -To accommodate authors who electronically typeset their manuscripts, -SIAM supports the use of \TeX. To ensure quality typesetting according -to SIAM style standards, SIAM provides a \TeX\ macro style file. -Using \TeX\ to format a manuscript should simplify the editorial process -and lessen the author's proofreading burden. However, -it is still necessary to proofread the galley proofs with care. - -Electronic files should not be submitted until the paper has been -accepted, and then not until requested to do so by someone in the SIAM -office. Once an article is slated for an issue, -someone from the SIAM office will contact the author about any or all -of the following: editorial and stylistic queries, -supplying the source files (and any supplementary macros) -for the properly formatted article, and handling figures. - -When submitting electronic files (electronic submissions) -(to {\tt tex@siam.org}) write the journal, issue, and author's -name in the subject line of the message. -Authors are responsible for ensuring that the paper generated -from the source files exactly matches the paper that -was accepted for publication by the review editor. If it does not, -information on how it differs should be indicated in the transmission -of the file. When submitting a file, please be sure to include any -additional macros (other than those provided by SIAM) that will be -needed to run the paper. - -SIAM uses MS-DOS-based computers for \TeX\ processing. Therefore -all filenames should be restricted to eight characters or less, -plus a three character extension. - -Once the files are corrected here at SIAM, we will mail the revised -proofs to be read against the original edited hardcopy -manuscript. We are not -set up to shuttle back and forth varying electronic versions of each -paper, so we must rely on hard copy of the galleys. The author's proofreading -is an important but easily overlooked step. Even if SIAM were not -to introduce a single editorial change into your manuscript, there -would still be a need to check, because electronic transmission -can introduce errors. - - -This distribution contains the following items: {\tt siamptex.sty}, the -main macro package; this documentation file; and a sample file {\tt -pexample.tex}. The sample file is representative of the standard way -to apply the macros. The rest of this paper emphasizes some aspects -of applying the macros, points out options and special cases, and -describes the SIAM style standards. -The SIAM macros make use of the small caps font, {\tt cmcsc}, which -is not installed in some systems. This font along with other -AMS-\TeX\ fonts can be retrieved from the American Mathematical -Society via anonymous FTP to {\tt e-math.ams.com}. - -\heading{2}{Headings} -The top matter of a journal is in a standard format. The macro -and initial definitions should be included as follows. - -\verbatim: -\input siamptex.sty -\overfullrule=0pt - -: - -The \verbatim:\overfullrule: should be set wider than zero points -while still being edited by the author to assist in locating -lines that extend beyond the margins. - - -The ``slugline,'' which contains the journal and copyright information, is -created by special commands following the \verbatim:\topmatter:. - -\verbatim: -\SIMAX -\vol{0} -\no{0, pp.~000--000} -\date{April 1995} -\copyyear{1995} -\code{000} - -: -Because authors will probably not know exact -volume, number, date, or code, insert zeros in their place as -above. SIAM will place the appropriate information in -the commands in production; however, the commands must be used. -\verbatim:\SIMAX:, \verbatim:\SIAP:, \verbatim:\SICOMP:, -\verbatim:\SICON:, \verbatim:\SIDMA:, \verbatim:\SIMA:, -\verbatim:\SIMAX:, \verbatim:\SINUM:, \verbatim:\SIOPT:, -\verbatim:\SISC:, and \verbatim:\SIREV: are the commands provided -to include the journal title in the heading. - -The title and author(s) of the paper are indicated by the -\verbatim:\title\endtitle: and \verbatim:\author\endauthor: commands. -Author support and address information is indicated as follows. - -\verbatim: -\author A.~U. Thorone\fnmark{$^{\dag}$} - \and A.~U. Thortwo\fnmark{$^{\ddag}$}\endauthor - -\address{$^{\dag}$}{Address of the first author and support} -\address{$^{\ddag}$}{Address of the second author and support} - -: - -If more than two authors are included, each should be separated -by a comma after the \verbatim:\fnmark{}: command. If more than one -author shares common footnote information, then a common footnote -and footnote mark should be used. - -The commands \verbatim:\shorttitle{}: and \verbatim:\shortauthor{}: -are used to designate the running heads for the paper. - -The \verbatim:\abstract{}:, \verbatim:\keywords\endkeywords:, and -\verbatim:\subjclass\endsubjclass:\break commands are used to include the -abstract, key words, and AMS subject classification numbers, respectively. -If there is to be only one subject classification number, the -\verbatim:\subjclass: command should be preceded by -\verbatim:\oneclass:. (If the AMS numbers are unknown, leave that -information blank.) Authors are responsible for providing AMS numbers. -They can be found in the Annual Index of Math Reviews or -through {\tt e-Math} ({\tt telnet e-math.ams.com}; login -and password are both {\tt e-math}). -Complete the topmatter section by including \verbatim:\endtopmatter:. - - - -\heading{3}{Equations and mathematics} -Equations and mathematics -are handled by standard \TeX\ commands. SIAM style is -for numbered equations to appear flush with the left margin. The -\verbatim:\leqno: and \verbatim:\leqalignno{}: commands are used for -this purpose. If any letters indicating subequations are to be used -with the numbers, they should be set in roman type. - -Clear equation formatting using \TeX\ can be challenging. Aside from -the regular \TeX\ documentation, authors will find Nicholas -J. Higham's book {\it Handbook of Writing for the Mathematical -Sciences\/} [1] useful for guidelines and tips on formatting with -\TeX. The book covers many other topics related to article -writing as well. - -Authors commonly make mistakes by using - \verbatim:<:, \verbatim:>:, \verbatim:\mid:, and -\verbatim:\parallel: as delimiters, instead of -\verbatim:\langle:, \verbatim:\rangle:, \verbatim:|:, -and \verbatim:\|:. The incorrect symbols have particular -meanings distinct from the correct ones and should not be confused. - -\bigskip -\eightpoint -\halign{#\hfil\quad&&#\hfil\quad\cr -&{\bf Wrong} &&&& {\bf Right}&\cr -&\verbatim:<x, y>: & $<x, y>$ &&& - \verbatim:\langle x, y\rangle: & $\langle x, y\rangle$ \cr -&\verbatim:5 < \mid A \mid: & $5 < \mid A \mid$ &&& - \verbatim:5 < |A|: & $5 < |A|$ \cr -& \verbatim:6x = \parallel x: \cr -&\verbatim: - 1\parallel_{i}: & $6x = \parallel x - 1\parallel_{i}$ &&& - \verbatim:6x = \|x - 1\|_{i}: & $6x = \| x - 1\|_{i}$\cr} - \tenpoint\rm -\bigskip - -Another common author error is to put large (and even medium sized) -matrices in-line with the text, rather than displaying them. This -creates unattractive line spacing problems, and should be assiduously -avoided. Text-sized matrices (like $({a \atop b} {b \atop c})$) might -be used but anything much more complex than the example cited will -not be easy to read and should be displayed. - -More information on the formatting of equations and aligned -equations is found in Knuth [2]. Authors bear primary responsibility -for formatting their equations within margins and in an aesthetically -pleasing and informative manner. - -The SIAM macros include additional roman math words, or ``log-like" -functions, to those provided in standard \TeX. The following -commands are added: \verbatim:\const:, \verbatim:\diag:, \verbatim:\grad:, -\verbatim:\Range:, \verbatim:\rank:, and \verbatim:\supp:. -These commands produce the same word as the command name -in math mode, in roman type. - - -Groups of equations that are not directly related to each other -should normally be centered independently. This may be done through -the \TeX\ math command \verbatim:\displaylines{}:. Numbering -independently centered equations can be difficult, so Seroul and -Levy's [3] macro \verbatim:\ldisplaylinesno{}: has been included -in {\tt siamptex.sty}. \verbatim:\ldisplaylinesno{}: works just -like \verbatim:\leqalignno:, except no ampersand is used to align -the equations, since they are to be centered. - -\heading{4}{Text formatting} -Section and subsection headings are both included using the -\verbatim:\heading{}{}: command, which requires two arguments. The -first argument is for the number, and the second -is the title of the section or -subsection. - -No extra spacing should be placed between paragraphs. The -\verbatim:\heading: command inserts the required spacing between -sections. - -SIAM style does not normally make use of plain \TeX's -\verbatim:\item: command. The \verbatim:\meti: command is preferred for -lists of items beginning with, for instance, bullets ($\bullet$) or -roman numerals (iv). The \verbatim:\meti: command retains normal -paragraph shape but places all labels aligned flush right. For -example: - -\verbatim: -\meti{(i)} This is the first item. -\meti{(ii)} This is the second item of the series. - -: - -produces - -\meti{(i)} This is the first item. -\meti{(ii)} This is the second item of the series. -\medskip - -The \verbatim:\meti: macro was adapted from Seroul and Levy [3]. - -\heading{4.1}{Punctuation} -All standard punctuation and all numerals should be set in roman type -(upright) even within italic text. -The only exceptions are periods and commas. They may -be set to match the surrounding text. - -References to sections should use the symbol \S, generated by -\verbatim:\S:. (If the reference begins a sentence, the term ``Section'' -should be spelled out in full.) Authors should not redefine -\verbatim:\S:, say, to be a calligraphic S, because \verbatim:\S: -must be reserved for use as the section symbol. - -Authors sometimes confuse the use of various types of dashes. -Hyphens (\verbatim:-:, -) are used for some compound words (many -such words should have no hyphen but must be run together, -like ``nonzero,'' or split apart, like ``well defined.'' -Minus signs (\verbatim:$-$:, $-$) -should be used in math to represent subtraction or negative numbers. -En dashes (\verbatim:--:, --) are used for ranges (like 3--5, -June--August), or for joined names (like Runge--Kutta). Em dashes -(\verbatim:---:, ---) are used to set off a clause---such as this -one---from the rest of the sentence. - -\heading{4.2}{Theorems, lemmas, and proofs} -Theorems, lemmas, propositions, and so forth, have macros included -for correct formatting. Below is an example. - -\verbatim: -\thm{Theorem 4.1} -Sample theorem included for illustration. -Numbers and parentheses, like equation $(3.2)$, should be set -in roman type. Note that words in displayed equations, such as -$$ x^2 = Y^2 \sin z^2 \hbox{ for all } x $$ -will appear in italic type in a theorem, though normally -they should appear in roman.\endthm - -: - -This sample produces Theorem 4.1 below. - -\thm{Theorem 4.1} -Sample theorem included for illustration. -Numbers and parentheses, like equation $(3.2)$, should be set -in roman type. Note that words in displayed equations, such as -$$ x^2 = Y^2 \sin z^2 \hbox{ for all } x $$ -will appear in italic type in a theorem, though normally -they should appear in roman.\endthm - - -The \verbatim:\cor:, \verbatim:\dfn:, \verbatim:\lem:, and -\verbatim:\prop: commands -all work similarly. Named theorems should be designated with the -title in roman type, enclosed in parentheses. - -\verbatim: -\thm{Theorem 3.2 {\rm (sample theorem with title)}} - -: - -Proofs are illustrated in the following example: - -\verbatim: -\prf{Proof} -The body of the proof. -\qquad\endproof - -: - -If the proof ends with a displayed equation, the \verbatim:\endproof: -box \endproof\ should appear two ems (\verbatim:\qquad:) -from the end of the equation on line with it horizontally. - -\heading{5}{Figures and tables} -Figures and tables are best handled in \TeX\ by putting them within a -\verbatim:\topinsert \endinsert: or \verbatim:\midinsert \endinsert: -environment. The appropriate amount -of space should be left for the figure, and the caption should be -formatted to be centered or as a paragraph if more than one line. Text -should be italic, eight-point type, with the words ``Fig.~\#'' in small -caps. A sample follows. - -\verbatim: -\midinsert -\vskip 22pc -\centerline{\eightpoint{\smc Fig.~5.1}. \it Italic caption text.} -\endinsert - -: - -SIAM tables should be formatted in eight-point type, with enough -space left between entries and surrounding lines so that they do not -touch. Take particular care with super- and subscript characters. -See Knuth [2] or Seroul and Levy [3] for more information on -the formatting of tables in \TeX. Table captions are similar to -figure captions, but the word ``Table'' and the number appear on -a separate line from the caption text. - -SIAM supports the use of {\tt psfig} for including {\smc PostScript} -figures. All {\smc Post\-Script} figures should be sent in separate -files. See the {\tt psfig} documentation (from wherever you acquired -{\tt psfig}) for more details on the use -of this style option. It is a good idea to submit high-quality -hardcopy of all {\smc Post\-Script} figures just in case there -is difficulty in the reproduction of the figure. Figures produced -by other non-\TeX\ methods should be included as high-quality -hardcopy when the manuscript is submitted. - -\heading{6}{Bibliographies} -References are handled using the \verbatim:\Refs: command. -All names are to be keyed initial upper case cap and small -caps. Only the first and middle initials, followed by the -last name, are to be used. Last names should never be listed first. -Some representative sample entries are illustrated below: - -\verbatim| -\Refs - -\ref 1\\ {\smc A.~U Thorone}, {\it Title of paper with lower case -letters}, SIAM J. Abbrev. Correctly, 2 (1992), pp.~000--000.\endref - -\ref 2\\ \sameauthor, % generates a 3-em rule -{\it Title of paper appearing in book}, in Book Title: -With All Initial Caps, Publisher, Location, 1992.\endref - -\ref 3\\ {\smc W. Riter}, -{\it Title of another paper appearing in a book}, in The Book -Title, E.~D. One, E.~D. Two, and A.~N. Othereditor, eds., -Publisher, Location, 1992, pp.~000--000.\endref - -\ref 4\\ {\smc A.~U. Thorone, A.~U. Thortwo, and A.~U. Thorthree}, -{\it Title of Book{\rm III:} Note Initial Caps}, -Publisher, Location, pp.~000--000, 1994.\endref - -\ref 5\\ {\smc A. Notherauth}, {\it Title of paper that's not yet -published}, SIAM J. Abbrev. Correctly, to appear.\endref -| - -Other types of references fall into the same general pattern. See the -sample file or any SIAM journal for other examples. Authors must -correctly format their bibliography to be considered as having used -the macros correctly. An incorrectly formatted bibliography is not -only time-consuming for SIAM to process -but it is possible that errors may be introduced by -keyboarders/copy editors. - -As an alternative to the above style of reference, an alphanumeric -code may be used in place of the number (e.g., [AUTh90]). The same -\verbatim:\Refs: and \verbatim:\ref: commands are used, but the -command \verbatim:\resetrefindent{}: must be used before the -\verbatim:\Refs: command, with the widest expected alphanumeric code -as an argument. - -Another alternative is no number, simply the authors' names and -the year of publication following in parentheses. The rest of the -format is identical. To get an entry with no number in brackets -before it, use the \verbatim:\xref: command. This method is acceptable -but not encouraged. - -\heading{7}{Conclusion} Many other style suggestions and tips -could be given to help authors but are beyond the scope of this -document. Simple mistakes can be avoided by increasing your familiarity -with how \TeX\ functions. The books referred to throughout this document -are also useful to the author who wants clear, beautiful typography -with minimal mistakes. - -\Refs - -\ref 1\\ {\smc N.~J. Higham}, {\it Handbook of Writing for -the Mathematical Sciences}, Society for Industrial and Applied -Mathematics, Philadelphia, PA, 1993.\endref - -\ref 2\\ {\smc D.~E. Knuth}, {\it The \TeX book}, Addison Wesley, -Reading, MA, 1986.\endref - -\ref 3\\ {\smc R. Seroul and S. Levy}, {\it A Beginner's Book of -{\rm \TeX}}, Springer-Verlag, Berlin, New York, 1991.\endref - - -\bye diff --git a/Master/texmf-dist/tex/plain/siam/pexample.tex b/Master/texmf-dist/tex/plain/siam/pexample.tex deleted file mode 100644 index eb2c2f50101..00000000000 --- a/Master/texmf-dist/tex/plain/siam/pexample.tex +++ /dev/null @@ -1,523 +0,0 @@ -% Sample file for SIAM's plain TeX macro package. -% 9-14-94 Paul Duggan -\input siamptex.sty - -% author defined macros included for illustrative purposes only. -% symbols for real numbers, complex, ... (\Bbb font from AMS-TeX -% fonts v2.x also usable) - -\def\fR{{\bf R}} -\def\fC{{\bf C}} -\def\fK{{\bf K}} - -% misc. operators -\def\Span {\mathop{\hbox{\rm span}}\nolimits} -\def\Range{\mathop{\hbox{\rm Range}}\nolimits} -\def\Det {\mathop{\hbox{\rm det}}} -\def\Re {\mathop{\hbox{\rm Re}}} -\def\Im {\mathop{\hbox{\rm Im}}} -\def\Deg {\mathop{\hbox{\rm deg}}} - -% misc. - -\def\Kr{\hbox{\bf K}} -\def\K { { K}} -\def\sT{\hbox{$\cal T$}} -\def\sB{\hbox{$\cal B$}} - -\def\bmatrix#1{\left[ \matrix{#1} \right]} - -% Each of the following commands have to be filled in with -% something. If the data is unknown, the arguments can be -% left blank. - -\topmatter -\journal{SIAM J. E{\smc XAMPLE} F{\smc ILES}} -\vol{1} -\no{1, pp.~000--000} -\date{October 1994} -\copyyear{1994} -\code{000} - - -\title SAMPLE FILE FOR SIAM PLAIN \TeX\ MACRO -PACKAGE\endtitle - -\shorttitle{SIAM MACRO EXAMPLE} - -\recdate{*}{October 1, 1994; accepted by the editors Month, x, -xxxx. This work was supported by the Society for Industrial -and Applied Mathematics, Philadelphia, Pennsylvania} - -\author Paul Duggan\fnmark{$^{\dag}$} \and Various A.~U. -Thors\fnmark{$^{\ddag}$}\endauthor - -\address{$^{\dag}$}{Composition Department, Society for -Industrial and Applied Mathematics, 3600 University City -Science Center, Philadelphia, Pennsylvania, 19104-2688 -({\tt duggan@siam.org})} - -\address{$^{\ddag}$}{Various affiliations, supported by -various foundation grants} - -\abstract{An example of SIAM \TeX\ macros is presented. -Various aspects of composing manuscripts for SIAM's journals -are illustrated with actual examples from accepted -manuscripts. SIAM's stylistic standards are adhered to -throughout, and illustrated.} - -\keywords polynomials, SI model\endkeywords - -\subjclass 33H40, 35C01\endsubjclass - -% if there is only one AMS subject number, the -% command \oneclass should precede the \subjclass command. - -\endtopmatter - -\heading{1}{Introduction and examples} -This paper presents a sample file for the use of SIAM's -\TeX\ macro package. It illustrates the features of the -macro package, using actual examples culled from various -papers published in SIAM's journals. This sample will provide -examples of how to use the -macros to generate standard elements of journal papers, -e.g., equations, theorems, or figures. This paper also -serves as an exmple of SIAM's stylistic preferences for the -formatting of such elements as bibliographic references, -displayed equations, and aligned equations, among others. -Some special circumstances are not dealt with this the -sample file; for that information, please see the -associated documentation file. - -{\it Note}. This paper is not to be read in any form for -content. The conglomeration of equations, lemmas, and other -text elements were put together solely for typographic -illustrative purposes. - -For theoretical reasons, it is desirable to find characterizations of the -conditions of breakdown of the algorithms that are based on the key {\it -spaces} $\Kr_n(r^{(0)},A)$ and $\Kr_n(\tilde r^{(0)},A^*)$ rather than -the {\it formulas} for the algorithms. In particular, we will -characterize breakdown of the three Lanczos algorithms in terms of the -{\it moment matrices} $\K_n(\tilde r^{(0)},A^*)^*\K_n(r^{(0)},A)$ and -$\K_n(\tilde r^{(0)},A^*)^*A\K_n(r^{(0)},A)$. Here we define the matrix -$\K_n(v,A)=\bmatrix{v&Av&\cdots&A^{n-1}v\cr}$, a matrix whose columns span -the Krylov space $\Kr_n(v,A)$. - -The following three theorems give exact conditions for breakdown of the -above algorithms. Detailed proofs may be found in [3]. A -result similar to Theorem 2 is found in [1]; see also [5]. - - -\thm{Theorem 1 {\rm (Lanczos--Orthodir breakdown)}} -Suppose Lanczos/Orthodir has successfully generated -$u^{(n-1)}\not=u$. Then the following are equivalent: - -\meti{$\bullet$} The algorithm does not break down at step $n$. - -\meti{$\bullet$} The matrix $\K_n(\tilde r^{(0)},A^*)^*A\K_n(r^{(0)},A)$ -is nonsingular. - -\meti{$\bullet$} There exists a unique iterate $u^{(n)}$ satisfying $(2)$. -\endthm - - -\thm{Theorem 2 {\rm (Lanczos--Orthomin breakdown)}} -Suppose Lanczos/Orthomin has successfully generated $u^{(n-1)}\not=u$. -Then the following are equivalent: - -\meti{$\bullet$} The algorithm breaks down at step $n$. - -\meti{$\bullet$} Either -$\K_{n-1}(\tilde r^{(0)},A^*)^*\K_{n-1}(r^{(0)},A)$ or -$\K_n(\tilde r^{(0)},A^*)^*A\K_n(r^{(0)},A)$ is singular. -\endthm - - -\prop{Proposition 3 {\rm (zero sets of polynomials)}} -Let $\fK=\fR$ or $\fC$. If $P$ is a complex nonzero polynomial in the -variables $x_1,x_2,\ldots ,x_N\in\fK$, then $P(x)\not=0$ for almost every -$x=(x_1,x_2,\ldots,x_N)\in \fK^N$. -\endprop - -\prf{Proof} -If $\fK=\fR$ and $P$ is nonzero, then either $\Re P(z)$ or $\Im P(z)$ -is a nonzero (real) polynomial; if $\fK=\fC$, we may decompose each $x_i$ -into real and imaginary parts, giving $2N$ variables, and consider the -real polynomial $P(x)^*P(x)$. In any case, we may assume without loss of -generality that $P$ is a nonzero real polynomial of real variables. - -We know that for any point $x$, the polynomial $P$ is the zero polynomial -if and only if the polynomial and all its derivatives are zero at $x$. -Let $V_0$ denote the set of zeros of $P$ in $\fR^N$. Suppose the set -$V_0$ has nonzero measure. We know from integration theory (see, for -example, [6, pp.\ 128f]) that almost every point of $V_0$ is -a point of density in each of the $N$ coordinate directions. We recall -that $x\in\fR$ is a point of density of a measurable subset -$S\subseteq\fR$ if for any sequence of intervals $I_n$ such that -$x\in I_n$ with measure $m(I_n)\rightarrow 0$ we have -$m(S\cap I_n)/m(I_n)\rightarrow 1$. - -It is easily seen that at such points in $V_0$, the first -partial derivatives of $P$ must necessarily be zero. Let $V_1$ be the -points of $V_0$ where all first derivatives are also zero. We have just -shown that $V_0$ and $V_1$ both have the same nonzero measure. The -argument -may be repeated for $V_1$ to show all second partial derivatives of $f$ -are zero at almost every point of $V_0$, and so forth, resulting in the -fact that $P$ and all its derivatives are zero on a set which has nonzero -measure. The proof is completed by selecting any one of these points. -\qquad\endproof - -\thm{Theorem 4 {\rm (Lanczos breakdown, iterate $n$)}} -Let $\fK=\fR$ or $\fC$, $A, \tilde Z\in\fK^{N\times N}$, and $n\leq d(A)$. -Then exactly one of the following three conditions holds for the Lanczos -method with $\tilde r^{(0)}=\tilde Z^* r^{(0)}$. - -\meti{\rm (i)} Hard breakdown at step $n$ occurs for every vector -$r^{(0)}\in\sT_n(A)\cap\fK^N$ $($and thus at least for almost every -$r^{(0)}\in\fK^N)$. - -\meti{\rm (ii)} Hard breakdown at step $n$ occurs for a nonempty measure-zero -set of vectors $r^{(0)}\in\sT_n(A)\cap\fK^N$ -$($and thus a nonempty measure-zero set of vectors in $\fK^N)$. - -\meti{\rm (iii)} Hard breakdown at step $n$ occurs for no vectors -$r^{(0)}\in\sT_n(A)\cap\fK^N$ $($and thus for at most a measure-zero set of -vectors in $\fK^N)$. - -Furthermore, the same result holds if ``hard breakdown'' is replaced by -``soft breakdown'' in the statement of this theorem. -\endthm - - -\prf{Proof} -For vectors $r^{(0)}\in\sT_n(A)\cap\fK^N$, breakdown is equivalent to -singularity of an appropriate moment matrix. The set $\sT_n(A)\cap\fK^N$ -amounts to almost -every vector in $\fK^N$. Now, by Corollary 5, the set $S_n$ of vectors in -$\fK^N$ for which the moment matrix of dimension $n$ is singular is either -the set of all vectors or a subset of measure zero. If the moment matrix -is singular for every vector (i.e., $S_n=\fK^N$), then it is singular for -every vector in $\sT_n(A)\cap\fK^N$, giving case (i) above. Otherwise the -set $S_n$ is measure zero in $\fK^N$. Thus -$\sB_n\equiv S_n\cap(\sT_n(A)\cap\fK^N)$ is of measure zero -and is either empty or nonempty. -\qquad\endproof - -\heading{2}{Tables and figures} -In Tables 1 and 2 we consider the unpreconditioned problem and also the (left) -ILU- and MILU-preconditioned problem (see [2] and [4]). Runs for which -convergence was not possible in ITMAX iterations are labeled by (--). - - -\topinsert -\hbox{\vbox{ \eightpoint -{\parindent 0pt -\centerline{\smc Table 1} -\centerline{\it Model problem, $h^{-1}=128$, {\rm ITMAX=3000}. - Number of iterations.}\vskip 6pt -\hfil\vbox{\offinterlineskip -\hrule -\halign{&\vrule#&\strut\ \hfil#\ \cr -height2pt&\omit&&\omit&&\omit&&\omit&&\omit - &&\omit&&\omit&&\omit&&\omit&&\omit&&\omit&\cr -&{\rm method $\backslash$ Dh: } & - &0&&2${}^{-3}$&&2${}^{-2}$&&2${}^{-1}$&&2${}^{0}$& - &2${}^{1}$&&2${}^{ 2}$&&2${}^{ 3}$&&2${}^{ 4}$&&2${}^{5}$&\cr -height2pt&\omit&&\omit&&\omit&&\omit&&\omit - &&\omit&&\omit&&\omit&&\omit&&\omit&&\omit&\cr -\noalign{\hrule} -height2pt&\omit&&\omit&&\omit&&\omit&&\omit - &&\omit&&\omit&&\omit&&\omit&&\omit&&\omit&\cr -&{GMRES}($\infty$) \hfill & -& 290&& 269&& 245&& 220&& 200&& 189&& 186&& 189&& 207&& 249&\cr -&{BCG} \hfill & -& 308&& 341&& 299&&1518&& -- && -- && -- && -- && 533&& -- &\cr -&{BCG}{\rm, random $u^{(0)}$} \hfill & -& 309&& 354&& 300&& 310&& 313&& 301&& 299&& 302&& 290&& 293&\cr -&{BCGNB} \hfill & -& 308&& 353&& 284&& 338&& 253&& 240&& 243&& 240&& 302&& 962&\cr -&{CGS} \hfill & -& 272&& 254&& 222&& -- && -- && -- && -- && -- && -- && -- &\cr -&{CGS}{\rm, random $u^{(0)}$} \hfill & -& 193&& 189&& 200&& 192&& 193&& 175&& 225&& 212&& 216&& 197&\cr -&{CGSNB} \hfill & -& 272&& 284&& 212&& 196&& 151&& 162&& 158&& 173&& 156&& 256&\cr -height1pt&\omit&&\omit&&\omit&&\omit&&\omit - &&\omit&&\omit&&\omit&&\omit&&\omit&&\omit&\cr -} \hrule}\hfil}}} -\endinsert - - -\topinsert - -\hbox{\vbox{ \eightpoint -{\parindent 0pt -\centerline{\smc Table 2} - -\centerline{\it Model Problem, $h^{-1}=128$,} -\centerline{\it {\rm MILU}-preconditioning, {\rm ITMAX=500.} -Number of iterations.} - -\medskip - -\hfil\vbox{\offinterlineskip -\hrule -\halign{&\vrule#&\strut\ \hfil#\ \cr -height2pt&\omit&&\omit&&\omit&&\omit&&\omit - &&\omit&&\omit&&\omit&&\omit&&\omit&&\omit&\cr -&{\rm Method $\backslash$ Dh: } & - &0&&2${}^{-3}$&&2${}^{-2}$&&2${}^{-1}$&&2${}^{0}$& - &2${}^{1}$&&2${}^{ 2}$&&2${}^{ 3}$&&2${}^{ 4}$&&2${}^{5}$&\cr -height2pt&\omit&&\omit&&\omit&&\omit&&\omit - &&\omit&&\omit&&\omit&&\omit&&\omit&&\omit&\cr -\noalign{\hrule} -height2pt&\omit&&\omit&&\omit&&\omit&&\omit - &&\omit&&\omit&&\omit&&\omit&&\omit&&\omit&\cr -&{\rm {GMRES}($\infty$)} \hfill & -& 27&& 25&& 24&& 26&& 28&& 28&& 25&& 19&& 14&& 10&\cr -&{\rm {GMRES}($\infty$), random $u^{(0)}$} \hfill & -& 33&& 29&& 28&& 29&& 31&& 31&& 29&& 24&& 19&& 14&\cr -&{\rm {BCG}} \hfill & -& 31&& 27&& 29&& 33&& 30&& 37&& 30&& 23&& 15&& 10&\cr -% &{BCG}, random $u^{(0)}$, $\gamma=.1$ \hfill & -% & 35&& 30&& 31&& 35&& 40&& 37&& 34&& 27&& 20&& 15&\cr -&{\rm {BCG}, random $u^{(0)}$} \hfill & -& 38&& 34&& 33&& 37&& 44&& 40&& 38&& 29&& 23&& 18&\cr -&{\rm {BCGNB}} \hfill & -& 28&& 27&& 29&& 30&& 34&& 35&& 30&& 23&& 15&& 10&\cr -&{\rm {CGS}} \hfill & -& 21&& 18&& 17&& 20&& 22&& 22&& 19&& 15&& 9&& 6&\cr -&{\rm {CGS}, random $u^{(0)}$} \hfill & -& 24&& 18&& 20&& 22&& 22&& 23&& 21&& 16&& 12&& 9&\cr -&{\rm {CGSNB}} \hfill & -& 21&& 18&& 17&& 20&& 22&& 27&& 20&& 15&& 9&& 6&\cr -height1pt&\omit&&\omit&&\omit&&\omit&&\omit - &&\omit&&\omit&&\omit&&\omit&&\omit&&\omit&\cr -} \hrule}\hfil}}} -\endinsert - -We make the following observations about these runs. - -\meti{$\bullet$} For the unpreconditioned problem, the standard -{BCG} and {CGS} algorithms break down in a number of cases, but the use -of random $u^{(0)}$ or the use of {BCGNB} or {CGSNB} -resulted in convergence. Furthermore, the iteration counts for the -algorithms {BCG} and {BCGNB} are in -general comparatively close to those of the ``best'' method, -{GMRES}($\infty$), while these algorithms have short economical -recurrences, unlike {GMRES}($\infty$). This underscores the -importance of the Lanczos algorithms as economical solution techniques. - -\meti{$\bullet$} For the ILU-preconditioned problems, in most cases -all methods worked well. For the case of $Dh=1$, {BCG} gave -an excessive number of iterations, but this was remedied significantly -by {BCGNB} and much more so -by the use of random $u^{(0)}$. Similarly, {CGS} could -not converge, but {CGSNB} and {CGS} with random -$u^{(0)}$ both converged. - -\meti{$\bullet$} For all of the MILU-preconditioned problems, all of -the Lanczos-type algorithms performed quite well. In particular, the -{BCG} algorithm gave approximately the same number of -iterations as {GMRES}($\infty$). - -Figures 1 and 2 give representative plots of the convergence behavior of the -algorithms for the case of $h^{-1}=128$, $Dh=4$, and no preconditioning. -These results show that the new algorithms keep the residual size -better behaved than the standard {BCG} and {CGS} -algorithms over the course of the run. - -\topinsert -\vskip 3.2in -\centerline{\eightpoint\smc Fig.~1. \it Residual -behavior: $h^{-1}=128$, $Dh=4$.} -\endinsert - - -\topinsert - \vskip 3.2in -\centerline{\eightpoint\smc Fig.~2. \it Residual -behavior: $h^{-1}=128$, $Dh=4$.} -\endinsert - -We now consider a more difficult class of finite difference problems, -namely, central finite differencing applied to the Dirichlet problem -$$ -u_{xx}(x,y) - u_{yy}(x,y) + - D[(y-\textstyle{1\over 2}\displaystyle) u_x(x,y) + - (x-\textstyle{1\over 3}\displaystyle) - (x-\textstyle{2\over 3}\displaystyle) u_y(x,y)], $$ -$$ - 43\pi^2u(x,y) = G(x,y) \quad {\rm on}\ \Omega=[0,1]^2,$$ -$$u(x,y) = 1 + xy \quad \hbox{\rm on}\ \partial\Omega,$$ -with $G(x,y)$ chosen as before so that the true solution is $u(x,y)=1+xy$. -Again, we let $h$ denote the mesh size in each direction. For $D=0$ -and $h$ small, the matrix generated by this problem is a symmetric -indefinite matrix with 16 distinct negative eigenvalues and the rest -of the spectrum positive. - -The standard conjugate residual algorithm applied to this problem with -$h^{-1}=128$ and $D=0$ requires 766 iterations to converge to -$||r^{(n)}||/||b||<\zeta=10^{-6}$. In any case, this is a difficult -problem to solve. - - \def\qed{\vrule height8pt width4pt depth0pt\par\medskip} - \def\Zero{{\bf 0}} - \def\dis{\displaystyle} - \def\b{\beta} - \def\r{\rho} - \def\X{{\bf X}} - \def\Y{{\bf Y}} - \def\bb{{\bar \beta}} - \def\tbcr{\theta\bb c_h \rho_h} - \def\ep{\varepsilon} - - - -Figures 3(a) and 3(b) show the compartmental diagrams for SI models without -and with deaths due to the disease, for the situation in which the infectious -period has only one stage. Figures 4(a) and 4(b) give the corresponding models -with $m$ stages of infection. Venereal -warts, caused by the human papilloma virus, and ordinary herpes are examples -of sexually transmitted diseases without deaths -due to the disease, although both are not quite SI diseases because of -partial immunity. AIDS is the example of an SI disease with death due to -the disease. Although our main focus is on the latter, we present results -on SI models without deaths due to the -disease because the simplification in the dynamics of such models - throws light on the case with disease-related deaths. - -\topinsert -\vskip 2in -\centerline{\eightpoint {\smc Fig.} 3(a). SI {\it model for subgroup $i$, without death -due to the disease.}} -\vskip 2in -\centerline{\eightpoint {\smc Fig.} 3(b). SI {\it model with death due to the disease.}} -\endinsert - -\topinsert -\vskip 2in -\centerline{\eightpoint {\smc Fig.} 4(a). SI {\it model without deaths due to the -disease with $m$ stages of infection.}} -\vskip 2in -\centerline{\eightpoint {\smc Fig.} 4(b). SI {\it model with deaths due to the disease, -with $m$ stages of infection.}} -\endinsert - -\heading{3}{Equations and alignments} -The equations for the system follow directly from the definitions and the -compartmental diagrams. For one infected stage with no disease-related -deaths, the equations are -$$ \dot X_i=-X_ig_i-\mu X_i+U_i, \leqno(1)$$ -$$ \dot Y_i=X_ig_i-\mu Y_i. \leqno(2)$$ -If there are multiple stages to the infection, (2) is replaced by -(3)--(5) as follows: -$$\leqalignno{\dot Y_{i1}&=X_ig_i-(k+\mu)Y_{i1}, &(3)\cr -\dot Y_{ir}&=kY_{i,r-1}-(k+\mu)Y_{ir},\qquad r=2,\ldots,m-1 &(4)\cr -\dot Y_{im}&=kY_{i,m-1}-\mu Y_{im}. &(5)\cr }$$ - - - -\heading{3.1}{The SI model with structured mixing} -In this subsection we write the equations for the SI model with -structured mixing, with one infected stage and with deaths due to the -disease. The equations for multiple infected stages follow easily, as do -those for SI models without death due to the disease. Recall that $f_{is}$ -gives the fraction of population subgroup $i$'s -contacts that are made in activity group $s$. The total contact rate of -susceptibles from population subgroup $i$ in activity group $s$ must be -$c_iX_if_{is}$. Let $\rho_{ij}(s)$ be the fraction of the contacts of group -$i$ that are with members of group $j$, within activity group $s$. -Assuming random allocation of the susceptibles and infecteds from each -population subgroup to the activity groups, the fraction infected in group -$j$ in activity group $s$ must be $Y_j/N_j$, giving -$$ c_iX_if_{is}\rho_{ij}(s)\beta_j{Y_j \over N_j}\leqno(6) $$ -for the rate at which susceptibles in $i$ are infected by contacts -with infecteds from $j$ in activity group $s$. Thus, in this case, $g_i$ is -given by -$$ - g_i=c_i\sum_sf_{is}\sum_j\rho_{ij}(s)\beta_j{Y_j \over N_j}, -\leqno(7) - $$ -and (1a) and (1b) become -$$ \dot X_i=-c_iX_i\sum_sf_{is}\sum_j\rho_{ij}(s)\beta_j{Y_j \over -N_j}-\mu X_i+U_i, \leqno(8) $$ -$$ \dot Y_i=c_iX_i\sum_sf_{is}\sum_j\rho_{ij}(s)\beta_j{Y_j \over -N_j}-(\mu+k)Y_i. \leqno(9) $$ - -\heading{3.2}{Structured mixing within activity groups} -If the mixing within activity groups is proportional mixing, then -$\rho_{ij}(s)$ is given by (10): -$$\rho_{ij}(s)={f_{js}c_jN_j\over \sum_pf_{ps}c_pN_p}, \leqno(10)$$ -and (8) and (9) become (11) and (12): -$$\dot X_i=-c_iX_i\sum_sf_{is}{\sum_jf_{js}c_j\beta_jY_j \over -\sum_jf_{js}c_jN_j}-\mu X_i+U_i \leqno(11)$$ -$$\dot Y_i=c_iX_i\sum_sf_{is}{\sum_jf_{js}c_j\beta_jY_j \over -\sum_jf_{js}c_jN_j}-(k+\mu)Y_i. \leqno(12)$$ - -Expressions (11) and (12) show an important consequence of death due -to the disease. If there are no deaths due to the disease, $N_j$ is -constant on the asymptotically stable invariant subspace $U_j=\mu -N_j$ for all $j$, and the first term, the nonlinear term, in -(11) and (12) is a sum of {\it quadratic} terms. If there are deaths -due to the disease, $N_j$ is no longer constant and the first term is -a sum of rational expressions, each homogeneous of degree one. This -observation extends to SIS, SIR, and SIRS models. - - - -\Refs - - -\ref 1\\ -{\smc R. Fletcher}, {\it Conjugate gradient methods for indefinite -systems}, in Numerical Analysis Dundee 1975, G.~A. Watson, ed., -Springer-Verlag, New York, Lecture Notes in Math. 506, -1976, pp. 73--89. -\endref - - -\ref 2\\ -{\smc I. Gustafsson}, {\it Stability and rate of convergence of -modified incomplete Cholesky factorization methods}, Ph.D. thesis, -Chalmers University of Technology and the University of Goteborg, -Goteborg, Sweden, 1979. -\endref - - -\ref 3\\ -{\smc W.~D. Joubert}, {\it Generalized conjugate gradient and -Lanczos methods for the solution of nonsymmetric systems of linear -equations}, Ph.D. thesis and Report -CNA-238, Center for Numerical Analysis, University of Texas, -Austin, TX, January 1990. -\endref - - -\ref 4\\ -{\smc J.~A. Meijerink and H.~A. van der Vorst}, {\it An iterative -solution method for linear systems of which the coefficient matrix is -a symmetric $M$-matrix}, Math. Comp., 31 (1977), pp.~148--162. -\endref - - - -\ref 5\\ -{\smc Y.~Saad}, {\it The Lanczos biorthogonalization algorithm and -other oblique projection methods for solving large unsymmetric systems}, -SIAM J. Numer. Anal., 19 (1982), pp. 485--506. -\endref - - -\ref 6\\ -{\smc S. Saks}, {\it The Theory of the Integral}, G.~E. Stechert, -New York, 1937. -\endref - -\ref 7\\ -{\smc M. Tinkham}, {\it Introduction to -Superconductivity}, McGraw-Hill, New York, 1975. -\endref - -\bye diff --git a/Master/texmf-dist/tex/plain/siam/siamptex.sty b/Master/texmf-dist/tex/plain/siam/siamptex.sty deleted file mode 100644 index 3ffce26af64..00000000000 --- a/Master/texmf-dist/tex/plain/siam/siamptex.sty +++ /dev/null @@ -1,373 +0,0 @@ -% SIAMPTEX.STY; 12-11-92; Paul Duggan, Society for Industrial -% and Applied Mathematics. From -% Ralph Youngen's siamtex.sty -% 9-14-94 ; Paul Duggan Revised. -% This file may be freely distributed but may not be altered in -% any way. -% -% This is a file of macros and definitions for creating an article -% for publication in a SIAM journal. -% -% Make the @ sign a letter for internal control sequences. -\catcode`\@=11 -% -% Report the version number of this package. -\message{ *** SIAM Plain TeX macro package, version - 2.1.1, SEPTEMBER-1994 ***} -% -%%% -%%% FONTS -%%% -\font\tenrm=cmr10 -\font\tenbf=cmbx10 -\font\tenit=cmti10 -\font\tentt=cmtt10 -\font\tensmc=cmcsc10 -\def\tenpoint{% - \def\rm{\fam0\tenrm}\def\bf{\fam\bffam\tenbf}% - \def\it{\fam\itfam\tenit}\def\smc{\tensmc}\def\tt{\tentt} - \textfont0=\tenrm \scriptfont0=\sevenrm - \textfont1=\teni \scriptfont1=\seveni - \textfont2=\tensy \scriptfont2=\sevensy - \textfont3=\tenex \scriptfont3=\tenex -\baselineskip=12pt\rm}% - -\font\ninerm=cmr9 -\font\ninebf=cmbx9 -\font\nineit=cmti9 -\def\ninepoint{% - \def\rm{\ninerm}\def\bf{\ninebf}% - \def\it{\nineit}\baselineskip=11pt\rm}% - -\font\eightrm=cmr8 -\font\eightbf=cmbx8 -\font\eightit=cmti8 -\font\eighti=cmmi8 -\font\eightsy=cmsy8 -\font\eightsmc=cmcsc10 at 8pt -\font\eighttt=cmtt8 - \def\eightpoint{% - \def\rm{\fam0\eightrm}\def\bf{\fam\bffam\eightbf}% - \def\it{\fam\itfam\eightit}\def\smc{\eightsmc}\def\tt{\eighttt} - \textfont0=\eightrm \scriptfont0=\sixrm - \textfont1=\eighti \scriptfont1=\sixi - \textfont2=\eightsy \scriptfont2=\sixsy -\textfont3=\tenex \scriptfont3=\tenex -\baselineskip=10pt\rm}% - -\font\sixrm=cmr6 -\font\sixbf=cmbx6 -\font\sixi=cmmi6 -\font\sixsmc=cmr5 -\font\sixsy=cmsy6 -\def\sixpoint{% - \def\rm{\sixrm}\def\bf{\sixbf}% - \def\smc{\sixsmc}\baselineskip=8pt\rm}% - -\fontdimen13\tensy=2.6pt -\fontdimen14\tensy=2.6pt -\fontdimen15\tensy=2.6pt -\fontdimen16\tensy=1.2pt -\fontdimen17\tensy=1.2pt -\fontdimen18\tensy=1.2pt - -\def\rheadfont{\eightpoint\rm} -\def\titlefont{\tenpoint\bf} -\def\authorfont{\eightpoint\smc} -\def\dedicatefont{\ninepoint\it} - - -%%% -%%% ROMAN PUNCTUATION -%%% (WARNING: may cause incompatibility with psfig) -%%% -\def\othersmcolon{;} -\catcode`\;= \active -\def;{\relax\ifmmode\othersmcolon - \else\ifdim\fontdimen1\the\font>0pt\/{\rm \othersmcolon}% - \else\othersmcolon\fi\fi} - - -%%% DIMENSIONS -%%% -\hsize=31pc -\vsize=50pc -\parindent=2em - - -%%% TOPMATTER MACROS -%%% -\newif\ifkeywords@ -\newif\ifsubjclass@ -\newif\ifdedicate@ -\newif\ifrecdate@ -\newif\ifoneclass@ - -\keywords@false -\subjclass@false -\dedicate@false -\recdate@false -\oneclass@false - -\def\title#1\endtitle{\def\thetitle{\uppercase{#1}}% - \def\\{\relax\ }\xdef\rightrh{\uppercase{#1}}} - -\def\shorttitle#1{\xdef\rightrh{\uppercase{#1}}} - -\let\protect\relax - -\def\author#1\endauthor{% - \def\and{\hbox{\sixrm AND }}\def\\{\break} - % prevent \uppercase when typesetting - \def\theauthor{\uppercase{#1}}% - {% - \def\\{\relax\ }% change \\ to be a space in the running head - \def\fnmark##1{}% turn address off in the running head - \def\and{and }% "and" is same size as names in running head - \def\protect{\noexpand\protect\noexpand} - \xdef\leftrh{\expandafter{\uppercase{#1}}}% - }} - -\def\shortauthor#1{\def\and{and }\xdef\leftrh{\uppercase{#1}}} - -\gdef\fnmark#1{#1} -\gdef\address#1#2{\makefootnote@{\textfont2=\eightsy #1}{#2\unskip.}} -\def\journal#1{\def\thejournal{#1}} -\def\SIMAC{\journal{SIAM J{\smc OURNAL} M{\smc ACRO}}} -\def\SIAP{\journal{SIAM J. A{\smc PPL.} M{\smc ATH.}}} -\def\SICOMP{\journal{SIAM J. C{\smc OMPUT.}}} -\def\SICON{\journal{SIAM J. C{\smc ONTROL} {\smc AND} O{\smc PTIMIZATION}}} -\def\SIDMA{\journal{SIAM J. D{\smc ISC.} M{\smc ATH.}}} -\def\SIMA{\journal{SIAM J. M{\smc ATH.} A{\smc NAL.}}} -\def\SIMAX{\journal{SIAM J. M{\smc ATRIX} A{\smc NAL.} A{\smc PPL.}}} -\def\SINUM{\journal{SIAM J. N{\smc UMER.} A{\smc NAL.}}} -\def\SIOPT{\journal{SIAM J. O{\smc PTIMIZATION}}} -\def\SISC{\journal{SIAM J. S{\smc CI.} C{\smc OMPUT.}}} -\def\SIREV{\journal{SIAM R{\smc EVIEW}}} - - -\def\copyyear#1{\def\thecopyyear{#1}} -\copyyear{1989} -\def\vol#1{\def\thevol{#1}} -\def\no#1{\def\theno{#1}} -\def\date#1{\def\thedate{#1}} -\def\code#1{\def\thecode{#1}} -\def\dedicate#1{\dedicate@true\def\thededicate{#1}} -\def\keywords#1\endkeywords{\keywords@true\def\thekeywords{#1}} -\def\subjclass#1\endsubjclass{\subjclass@true\def\thesubjclass{#1}} -\def\oneclass{\oneclass@true} -\long\def\abstract#1{\def\theabstract{#1}} - -\def\raggedcenter{\leftskip=0pt plus 1fill \rightskip=0pt plus 1fill} - -\def\copyright#1{{\ooalign{\hfil\raise.07ex\hbox{c}\hfil\crcr#1\char"0D}}} - -\def\recdate#1#2{\global\recdate@true - \gdef\recdate@{#1Received by the editors \ignorespaces#2\unskip.}% - \makefootnote@{}{\recdate@}} - -\let\topmatter=\relax -\def\endtopmatter{% - \global\headline={\hss\vtop to \z@ {% - \sixpoint\rm\noindent\thejournal \hfill% - \rm\copyright{\sevensy}\rm% - \ \thecopyyear\ Society for Industrial and Applied Mathematics\par - \noindent Vol. \thevol , No. \theno , \thedate\hfill\thecode\par - \vss}\hss}% - \leavevmode\vskip8pt - \vbox{\noindent\raggedcenter\let\\=\break\titlefont\thetitle - \ifrecdate@*\fi} - \vskip6pt - \vbox{\noindent\raggedcenter\let\\=\break\authorfont\theauthor} - \ifdedicate@ - \vskip6pt - \vbox{\noindent\raggedcenter\let\\=\break\dedicatefont - \thededicate} - \fi - \vskip14pt - {\eightpoint{\bf Abstract.\ }\theabstract\par - \ifkeywords@ - \vskip10pt - {\bf Key words.} \thekeywords\par - \fi - \ifsubjclass@ - \vskip10pt - {\bf AMS subject classification\ifoneclass@\else s\fi. }% - \thesubjclass\par - \fi} - \vskip8pt - \tenpoint} - - -%%% THEOREM AND OTHER MACROS -%%% -\def\heading#1#2{% - \vskip6pt{\bf #1.\enspace\ignorespaces#2.\enspace}\ignorespaces} - -\def\thm#1{{\smc #1.}\begingroup\it\enspace\ignorespaces} -\let\lem=\thm -\let\cor=\thm -\let\prop=\thm -\let\dfn=\thm - -\def\endthm{\endgroup} -\let\endlem=\endthm -\let\endcor=\endthm -\let\endprop=\endthm -\let\enddfn=\endthm - -\def\prf#1{{\it #1}.\rm\enspace\ignorespaces} -\let\rem=\prf -\let\case=\prf - -\def\endproof{\vbox{\hrule height0.8pt\hbox{% - \vrule height1.3ex width0.8pt\hskip0.8ex - \vrule width0.8pt}\hrule height0.8pt - }} - - -%%% FORMATTING AND MATH -%%% -%%% NEW ROMAN MATH OPERATORS -%%% -\def\const{\mathop{\rm const}\nolimits} -\def\diag{\mathop{\rm diag}\nolimits} -\def\grad{\mathop{\rm grad}\nolimits} -\def\Range{\mathop{\rm Range}\nolimits} -\def\rank{\mathop{\rm rank}\nolimits} -\def\supp{\mathop{\rm supp}\nolimits} - -%%% Centered displays, with numbering -%%% - -\def\ldisplaylinesno#1{\displ@y\halign{ - \hbox to\displaywidth{$\@lign\hfil\displaystyle##\hfil$}& - \kern-\displaywidth\rlap{$##$}\kern\displaywidth\crcr - #1\crcr}} - -%%% \meti to be used instead of \item -%%% -\def\meti#1{\parindent=2\parindent -\par\indent\llap{#1\enspace}\ignorespaces\parindent=.5\parindent} -\def\metimeti#1{\parindent=2\parindent -\par\indent\llap{#1\enspace}\ignorespaces\parindent=.5\parindent} - - -%%% Miscellaneous - -%%% REFERENCES - -\newdimen\refindent@ -\newdimen\refhangindent@ -\newbox\refbox@ -\setbox\refbox@=\hbox{\eightpoint\rm [00]}% Default 2 digits -\refindent@=\wd\refbox@ - -\def\resetrefindent#1{% - \setbox\refbox@=\hbox{\eightpoint\rm [#1]}% - \refindent@=\wd\refbox@} - -\def\Refs{% - \unskip\vskip2pc - \centerline{\eightpoint\rm REFERENCES}% - \penalty10000 - \vskip4pt - \penalty10000 - \refhangindent@=\refindent@ - \global\advance\refhangindent@ by 2em - \global\everypar{\hangindent\refhangindent@}% - \parindent=0pt\eightpoint\rm} - -\def\XRefs{% - \unskip\vskip2pc - \centerline{\eightpoint\rm REFERENCES}% - \penalty10000 - \vskip4pt - \penalty10000 - \refhangindent@=\refindent@ - \global\everypar{\hangindent\refhangindent@}% - \parindent=0pt\eightpoint\rm} - -\def\sameauthor{\leavevmode\vbox to 1ex{\vskip 0pt plus 100pt - \hbox to 3em{\leaders\hrule\hfil}\vskip 0pt plus 300pt}} - -\def\ref#1\\#2\endref{\leavevmode\hbox to \refindent@{\hfil[#1]}\enspace #2\par} - -\def\xref\\#1\endref{\leavevmode #1\par} - -%%% OUTPUT - -\global\footline={\hss\eightpoint\rm\folio\hss}% first page -\output{\plainoutput} -\def\plainoutput{\shipout\vbox{\makeheadline\pagebody\makefootline}% - \advancepageno - \ifnum\pageno>1 - \global\footline={\hfill}% - \fi - \ifodd\pageno - \global\headline={\hss\rightrh\hss{\tenpoint\rm\folio}}% - \else - \global\headline={\hskip-8pt{\tenpoint\rm\folio}\hss\leftrh\hss}% - \fi - \ifnum\outputpenalty>-\@MM \else\dosupereject\fi} -\def\pagebody{\vbox to\vsize{\boxmaxdepth\maxdepth \pagecontents}} -\def\makeheadline{\vbox to\z@{\vskip-22.5\p@ - \line{\vbox to8.5\p@{}\rheadfont\the\headline}\vss}% - \nointerlineskip} -\def\makefootline{\baselineskip24\p@\vskip-8\p@\line{\the\footline}} -\def\dosupereject{\ifnum\insertpenalties>\z@ % something is being held over - \line{}\kern-\topskip\nobreak\vfill\supereject\fi} - -\def\relaxnext@{\let\next\relax} -\def\footmarkform@#1{\ifmmode {}^{#1}\else$^{#1}$\fi } -\let\thefootnotemark\footmarkform@ -\def\makefootnote@#1#2{\insert\footins - {\interlinepenalty\interfootnotelinepenalty - \eightpoint \splittopskip=\ht\strutbox - \splitmaxdepth=\dp\strutbox - \floatingpenalty=\@MM - \leftskip=\z@ \rightskip=\z@ - \spaceskip=\z@ \xspaceskip=\z@ - \leavevmode{#1}\footstrut\ignorespaces#2\unskip - \lower\dp\strutbox\vbox to\dp\strutbox{}}} -\newcount\footmarkcount@ - \footmarkcount@=\z@ % Initialization -\def\footnotemark{\let\@sf=\empty \relaxnext@ - \ifhmode \edef\@sf{\spacefactor=\the\spacefactor}\/\fi - \def\next@{\ifx[\next \let\next=\nextii@ \else - \ifx"\next \let\next=\nextiii@ \else - \let\next=\nextiv@ \fi\fi\next}% - \def\nextii@[##1]{\footmarkform@{##1}\@sf}% - \def\nextiii@"##1"{{##1}\@sf}% - \def\nextiv@{\global\advance\footmarkcount@\@ne - \footmarkform@{\number\footmarkcount@}\@sf}% - \futurelet\next\next@} -\def\footnotetext{\relaxnext@ - \def\next@{\ifx[\next \let\next=\nextii@ \else - \ifx"\next \let\next=\nextiii@ \else - \let\next=\nextiv@ \fi\fi\next}% - \def\nextii@[##1]##2{\makefootnote@{\footmarkform@{##1}}{##2}}% - \def\nextiii@"##1"##2{\makefootnote@{##1}{##2}}% - \def\nextiv@##1{\makefootnote@{\footmarkform@{% - \number\footmarkcount@}}{##1}}% - \futurelet\next\next@} -\def\footnote{\let\@sf=\empty \relaxnext@ - \ifhmode \edef\@sf{\spacefactor\the\spacefactor}\/\fi - \def\next@{\ifx[\next \let\next=\nextii@ \else - \ifx"\next \let\next=\nextiii@ \else - \let\next=\nextiv@ \fi\fi\next}% - \def\nextii@[##1]##2{\footnotemark[##1]\footnotetext[##1]{##2}}% - \def\nextiii@"##1"##2{\footnotemark"##1"\footnotetext"##1"{##2}}% - \def\nextiv@##1{\footnotemark\footnotetext{##1}}% - \futurelet\next\next@} -\def\adjustfootnotemark#1{\advance\footmarkcount@#1\relax} - -\skip\footins=18\p@ plus6\p@ minus6\p@ - -\def\footnoterule{\kern -4\p@\hrule width 3pc \kern 3.6\p@ } % rule = .4 pt high - - - -% Turn off @ as being a letter. -% -\catcode`\@=12 diff --git a/Master/texmf-dist/tpm/siam.tpm b/Master/texmf-dist/tpm/siam.tpm deleted file mode 100644 index b6f773a402b..00000000000 --- a/Master/texmf-dist/tpm/siam.tpm +++ /dev/null @@ -1,57 +0,0 @@ -<!DOCTYPE rdf:RDF SYSTEM "../../support/tpm.dtd"> -<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:TPM="http://texlive.dante.de/"> - <rdf:Description about="http://texlive.dante.de/texlive/Package/siam.zip"> - <TPM:Name>siam</TPM:Name> - <TPM:Type>Package</TPM:Type> - <TPM:Date>2006/01/11 23:57:47</TPM:Date> - <TPM:Version></TPM:Version> - <TPM:Creator>rahtz</TPM:Creator> - <TPM:Title>Styles for SIAM publications.</TPM:Title> - <TPM:Description> -Packages for plain TeX and both LaTeX and old LaTeX 2.09, with -instructions for submissions. -[description copied from TeX Catalogue] - </TPM:Description> - <TPM:Author>unknown</TPM:Author> - <TPM:Size>495409</TPM:Size> - <TPM:License></TPM:License> - <TPM:Build/> - <TPM:RunFiles size="142878"> -texmf-dist/tex/amstex/siam/amsamp.tex -texmf-dist/tex/amstex/siam/amstexsi.sty -texmf-dist/tex/amstex/siam/siamdoc.tex -texmf-dist/tex/latex/siam/numinsec.sty -texmf-dist/tex/latex/siam/siam10.clo -texmf-dist/tex/latex/siam/siam10.sty -texmf-dist/tex/latex/siam/siam11.sty -texmf-dist/tex/latex/siam/siamltex.cls -texmf-dist/tex/latex/siam/siamltex.sty -texmf-dist/tex/latex/siam/subeqn.clo -texmf-dist/tex/plain/siam/docuptex.tex -texmf-dist/tex/plain/siam/pexample.tex -texmf-dist/tex/plain/siam/siamptex.sty -texmf-dist/tpm/siam.tpm - </TPM:RunFiles> - <TPM:DocFiles size="64673"> -texmf-dist/doc/amstex/siam/amsamp.tex -texmf-dist/doc/latex/siam/READ.ME -texmf-dist/doc/latex/siam/docultex.tex -texmf-dist/doc/latex/siam/lexample.tex - </TPM:DocFiles> - <TPM:SourceFiles size="287858"> -texmf-dist/source/latex/siam/ltexconf.all -texmf-dist/source/latex/siam/ltexnec.all -texmf-dist/source/latex/siam/ltexpprt.all -texmf-dist/source/latex/siam/ltexproc.all -texmf-dist/source/latex/siam/ptexconf.all -texmf-dist/source/latex/siam/ptexnec.all -texmf-dist/source/latex/siam/ptexpprt.all -texmf-dist/source/latex/siam/ptexproc.all -texmf-dist/source/latex/siam/soda209.all -texmf-dist/source/latex/siam/soda2e.all -texmf-dist/source/latex/siam/sodaptex.all - </TPM:SourceFiles> - <TPM:Provides>Package/siam</TPM:Provides> - </rdf:Description> -</rdf:RDF> - |