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-rw-r--r--Master/texmf-dist/doc/amstex/siam/amsamp.tex365
-rw-r--r--Master/texmf-dist/doc/latex/siam/READ.ME38
-rw-r--r--Master/texmf-dist/doc/latex/siam/docultex.tex592
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-% 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
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-%%
-%% 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}
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-Gritzmann and B. Sturmfels, eds., American Mathematical
-Society, Providence, RI, 1991, pp. 117--134.
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-{\em Strong forms of nonsingularity}, Linear Algebra Appl.,
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-determinant}, Proc. Amer. Math. Soc., 27 (1971),
-pp.~471--476.
-
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-{\sc V.~Klee, R.~Ladner, and R.~Manber}, {\it
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-(1984), pp.~131--157.
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-{\sc K. Murota}, LU-{\em decomposition of a matrix with
-entries of different kinds}, Linear Algebra Appl., 49
-(1983), pp.~275--283.
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-{\sc O.~Axelsson}, {\em Conjugate gradient type methods for unsymmetric and
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- pp.~1--16.
-
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-{\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.
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-\bibitem{DES}
-{\sc R.~S. Dembo, S.~C. Eisenstat, and T.~Steihaug}, {\em Inexact {N}ewton
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-{\sc S.~C. Eisenstat, H.~C. Elman, and M.~H. Schultz}, {\em Variational
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-{\sc H.~C. Elman}, {\em Iterative methods for large, sparse, nonsymmetric
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-
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-{\sc R.~Glowinski, H.~B. Keller, and L.~Rheinhart}, {\em Continuation-conjugate
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- problems}, SIAM J. Sci. Statist. Comput., 6 (1985), pp.~793--832.
-
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-{\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}
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- Comput., 7 (1986), pp.~856--869.
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-\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.
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-\bibitem{Walker89}
-\sameauthor, {\em Implementations of
- the {\rm GMRES} method}, Computer Phys. Comm., 53 (1989), pp.~311--320.
-
-\end{thebibliography}
-
-\end{document}
-
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--- a/Master/texmf-dist/source/latex/siam/ltexconf.all
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@@ -1,112 +0,0 @@
-
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-
-
-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
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-\font\tensmc=cmcsc10
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-
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- \belowdisplayskip\z@
- \abovedisplayshortskip\abovedisplayskip
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- \itemsep \parsep}}
-
-\let\referencesize\footnotesize
-
-\footnotesep 0pt
-
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-
-\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
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- \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}
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-\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}}}
-
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-{\@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
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-% 1/30/86 (HWT) Original version, by Howard Trickey.
-% 6/15/87 (HWT) Fix format.editors---Martin Costabel.
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- '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}
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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
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-\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@
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-\addvspace{3pt}\nopagebreak\list
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-\small}
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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
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-\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
-%
-
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-\message{*** ACM/SIAM Plain TeX Preprint Series macro package, version 1.0,
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-
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-%
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-%%% THEOREMS, PROOFS, DEFINITIONS, etc. %%%
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-
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-%%% FIGURES AND CAPTIONS %%%
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-
-\def\ref#1\\#2\endref{\leavevmode\hbox to \refindent@{\hfil[#1]}\enspace #2\par}
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-
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-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
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- \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/">
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- <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">
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-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
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