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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
deleted file mode 100644
index 811a058cc91..00000000000
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+++ /dev/null
@@ -1,592 +0,0 @@
-%%
-%% This is file `docultex.tex', 
-%% Documentation for siam macros for use with LaTeX 2e
-%% 
-%% By Paul Duggan for the Society for Industrial and Applied
-%% Mathematics. 
-%% 
-%% December 1, 1995
-%%
-%% Version 1.0a
-%% 
-%% You are not allowed to change this file. 
-%% 
-%% You are allowed to distribute this file under the condition that 
-%% it is distributed together with all of the files in the siam macro 
-%% distribution. These are:
-%%
-%%  siamltex.cls (main LaTeX macro for SIAM)
-%%  siamltex.sty (includes siamltex.cls for compatibility mode)
-%%  siam10.clo   (size option for 10pt papers)
-%%  subeqn.clo   (allows equation numbners with lettered subelements)
-%%  siam.bst     (bibliographic style file for BibTeX)
-%%  docultex.tex (this file)
-%%  lexample.tex (example file for latex macro)
-%%
-%% If you receive only some of these files from someone, complain! 
-%% 
-%% You are NOT ALLOWED to distribute this file alone. You are NOT 
-%% ALLOWED to take money for the distribution or use of either this 
-%% file or a changed version, except for a nominal charge for copying 
-%% etc. 
-%% \CharacterTable
-%%  {Upper-case    \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z
-%%   Lower-case    \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z
-%%   Digits        \0\1\2\3\4\5\6\7\8\9
-%%   Exclamation   \!     Double quote  \"     Hash (number) \#
-%%   Dollar        \$     Percent       \%     Ampersand     \&
-%%   Acute accent  \'     Left paren    \(     Right paren   \)
-%%   Asterisk      \*     Plus          \+     Comma         \,
-%%   Minus         \-     Point         \.     Solidus       \/
-%%   Colon         \:     Semicolon     \;     Less than     \<
-%%   Equals        \=     Greater than  \>     Question mark \?
-%%   Commercial at \@     Left bracket  \[     Backslash     \\
-%%   Right bracket \]     Circumflex    \^     Underscore    \_
-%%   Grave accent  \`     Left brace    \{     Vertical bar  \|
-%%   Right brace   \}     Tilde         \~}
-
-\documentclass[final]{siamltex}
-
-\title{USING SIAM'S \LaTeX\ MACROS\thanks{This work was
-supported by the Society for Industrial and Applied
-Mathematics}} 
-
-\author{Paul Duggan\thanks{Society for Industrial and
-Applied Mathematics, Philadelphia, Pennsylvania. 
-(duggan@siam. org). Questions, comments, or corrections
-to this document may be directed to that email address.}}
-
-
-\begin{document}
-\maketitle
-
-\begin{abstract}
-Documentation is given for use of the SIAM \LaTeX\ macros. These
-macros are now compatible with \LaTeX$2_{\varepsilon}$.
-Instructions and suggestions for compliance with SIAM style
-standards are also included. Familiarity with standard \LaTeX\ commands
-is assumed.
-\end{abstract}
-
-\begin{keywords}\end{keywords}
-
-\begin{AMS}\end{AMS}
-
-
-\pagestyle{myheadings}
-\thispagestyle{plain}
-\markboth{PAUL DUGGAN}{USING SIAM'S \LaTeX\ MACROS}
-
-\section{Introduction}
-
-This file is documentation for the SIAM \LaTeX\ macros, and
-provides instruction for submission of your files.
-
-To accommodate authors who electronically typeset their manuscripts,
-SIAM supports the use of \LaTeX. To ensure quality typesetting according
-to SIAM style standards, SIAM provides a \LaTeX\ macro style file.
-Using \LaTeX\ to format a manuscript should simplify the editorial process
-and lessen the author's proofreading burden. However,
-it is still necessary to proofread the galley proofs with care.
-
-Electronic files should not be submitted until the paper has been
-accepted, and then not until requested to do so by someone in the SIAM
-office. Once an article is slated for an issue,
-someone from the SIAM office will contact the author about any or all
-of the following: editorial and stylistic queries, 
-supplying the source files (and any supplementary macros)
-for the properly formatted article, and handling figures.
-
-When submitting electronic files  (electronic submissions) 
-(to {\tt tex@siam.org}) include  the journal, issue, and author's
-name in the subject line of the message. 
-Authors are responsible for ensuring  that the paper generated 
-from the source files exactly matches the paper that
-was accepted for publication by the review editor. If it does not,
-information on how it differs should be indicated in the transmission 
-of the file. When submitting a file, please be sure to include any 
-additional macros (other than those provided by SIAM) that will be 
-needed to run the paper. 
-
-SIAM uses MS-DOS-based computers for \LaTeX\ processing. Therefore
-all filenames should be restricted to eight characters or less,
-plus a three character extension.
-
-Once the files are corrected here at SIAM, we will mail the revised 
-proofs to be read against the original edited hardcopy 
-manuscript. We are not
-set up to shuttle back and forth varying electronic versions of each
-paper, so we must rely on hard copy of the galleys. The author's proofreading
-is an important but easily overlooked step. Even if SIAM were not
-to introduce a single editorial change into your manuscript, there
-would still be a need to check, because electronic transmission
-can introduce errors.
-
-The distribution contains the following items: {\tt
-siamltex.cls}, the main macro package based on {\tt
-article.cls}; {\tt siam10.clo}, for the ten-point size option;\linebreak 
-{\tt subeqn.clo}, a style option for equation numbering (see \S3 for
-an explanation); and  {\tt siam.bst},
- the style file for use with {\sc Bib}\TeX. Also included are this
-file {\tt docultex.tex} and a sample file {\tt lexample.tex}.
-The sample file represents a standard application of 
-the macros. The rest of this paper will highlight
-some keys to effective macro use, as well as point out options and
-special cases, and describe SIAM style standards to which
-authors should conform.
-
-
-\section{Headings}
-The top matter of a journal paper falls into a standard
-format. It begins of course with the \verb|\documentclass| command
-
-\begin{verbatim}
-
-\documentclass{siamltex}
-
-\end{verbatim}
-
-Other class options  can be included
-in the bracketed argument of the command, separated by commas.
-
-
-The title and author parts are formatted using the
-\verb|\title| and \verb|\author| commands as described in Lamport
-\cite{Lamport}. The \verb|\date|
-command is not used. \verb|\maketitle| produces the actual
-output of the commands.
-
-The addresses and support acknowledgments are put into the
-\verb|\author| commands via \verb|\thanks|. If support is
-overall for the authors, the support acknowledgment should
-be put in a \verb|\thanks| command in the \verb|\title|.
-Specific support should go following the addresses of the
-individual authors in the same \verb|\thanks| command.
-
-Sometimes authors have support or addresses in common which
-necessitates having multiple \verb|\thanks| commands for
-each author. Unfortunately \LaTeX\ does not normally allow this, 
-so a special procedure must be used. An example of this procedure
-follows. Grant information can also be run into both authors' 
-footnotes.
-
-\begin{verbatim}
-
-\title{TITLE OF PAPER}
-
-\author{A.~U. Thorone\footnotemark[2]\ \footnotemark[5]
-\and A.~U. Thortwo\footnotemark[3]\ \footnotemark[5]
-\and A.~U. Thorthree\footnotemark[4]}
-
-\begin{document}
-\maketitle
-
-\renewcommand{\thefootnote}{\fnsymbol{footnote}}
-
-\footnotetext[2]{Address of A.~U. Thorone}
-\footnotetext[3]{Address of A.~U. Thortwo}
-\footnotetext[4]{Address of A.~U. Thorthree}
-\footnotetext[5]{Support in common for the first and second
-authors.}
-
-\renewcommand{\thefootnote}{\arabic{footnote}}
-
-\end{verbatim}
-
-Notice that the footnote marks begin with {\tt [2]}
-because the first mark (the asterisk) will be used in the
-title for date-received information by SIAM, even if not
-already used for support data. This is just one example;
-other situations follow a similar pattern.
-
-Following the author and title is the abstract, key words
-listing, and AMS subject classification number(s),
-designated using the \verb|{abstract}|, \verb|{keywords}|,
-and \verb|{AMS}| environments. If
-there is only one AMS number, the commands
-\verb|\begin{AM}| and \verb|\end{AM}| are used
-instead of \verb|{AMS}|. This causes the heading to be
-in the singular. Authors are responsible for providing AMS numbers.
-They can be found in the Annual Index of Math Reviews, or
-through {\tt e-Math} ({\tt telnet e-math.ams.com}; login
-and password are both {\tt e-math}).   
-
-Left and right running heads should be provided in the
-following way.
-
-\begin{verbatim}
-
-\pagestyle{myheadings}
-\thispagestyle{plain}
-\markboth{A.~U. THORONE AND A.~U. THORTWO}{SHORTER PAPER
-TITLE} 
-
-\end{verbatim}
-
-\section{Equations and mathematics}
-
-One advantage of \LaTeX\ is that it can automatically number
-equations and refer to these equation numbers in text. While plain \TeX's
-method of equation numbering (explicit numbering using
-\verb|\leqno|) works in the SIAM macro, it is not preferred
-except in certain cases. SIAM style guidelines call for
-aligned equations in many circumstances, and \LaTeX's 
-\verb|{eqnarray}| environment is not compatible with
-\verb|\leqno| and \LaTeX\ is not compatible with the plain
-\TeX\ command \verb|\eqalign| and \verb|\leqalignno|. Since
-SIAM may have to alter or realign certain groups of
-equations, it is necessary to use the \LaTeX\ system of
-automatic numbering.
-
-Sometimes it is desirable to designate subequations of a larger
-equation number. The subequations are designated with
-(roman font) letters appended after the number. SIAM has
-supplemented its macros with the {\tt subeqn.clo} option which
-defines the environment \verb|{subequations}|.
-
-\begin{verbatim}
-
-\begin{subequations}\label{EKx}
-\begin{equation}
- y_k =  B  y_{k-1} +  f, \qquad k=1,2,3,\ldots  
-\end{equation}
-for  any initial vector $ y_0$.   Then 
-\begin{equation}
- y_k\rightarrow  u \mbox{\quad iff\quad} \rho( B)<1.
-\end{equation}
-\end{subequations}
-
-\end{verbatim}
-
-All equations within the \verb|{subequations}| environment
-will keep the same overall number, but the letter
-designation will increase.
-
-Clear equation formatting using \TeX\ can be challenging. Aside from
-the regular \TeX\ documentation, authors will find Nicholas 
-J. Higham's book {\em Handbook of Writing for the Mathematical
-Sciences\/} \cite{Higham} useful for guidelines and tips on 
-formatting with \TeX. The book covers many other topics related 
-to article writing as well.                
-
-Authors commonly make mistakes by using
- \verb|<|, \verb|>|, \verb|\mid|, and 
-\verb|\parallel| as delimiters, instead of 
-\verb|\langle|, \verb|\rangle|, \verb:|:,
-and \verb:\|:. The incorrect symbols have particular 
-meanings distinct from the correct ones and should not be confused.
-
-\begin{table}[htbp]
-\caption{Illustration of incorrect delimiter use.}
-\begin{center}\footnotesize
-\renewcommand{\arraystretch}{1.3}
-\begin{tabular}{|ll|ll|}\hline
-\multicolumn{2}{|c|}{{\bf Wrong}} & \multicolumn{2}{c|}{{\bf Right}}\\ \hline
-\verb|<x, y>| & $<x, y>$   &  \verb|\langle x, y\rangle| & $\langle x, y\rangle$\\
-\verb|5 < \mid A \mid| &  $5 < \mid A \mid$ & \verb:5 < |A|: &  $5 < |A|$\\
-\verb|6x = \parallel x|&&&\\ 
-\verb|    - 1\parallel_{i}| & $6x = \parallel x - 1\parallel_{i}$ &
-   \verb:6x = \|x - 1\|_{i}: & $6x = \| x - 1\|_{i}$\\ \hline
-\end{tabular}
-\end{center}
-\end{table}
-
-Another common author error is to put large (and even medium sized)
-matrices in-line with the text, rather than displaying them. This
-creates unattractive line spacing problems, and should be assiduously
-avoided. Text-sized matrices (like $({a \atop b} {b \atop c})$) might
-be used but anything much more complex than the example cited will
-not be easy to read and should be displayed.
-
-More information on the formatting of equations and aligned
-equations is found in Lamport \cite{Lamport}. Authors bear 
-primary responsibility for formatting their equations within 
-margins and in an aesthetically pleasing and informative manner.
-
-The SIAM macros include additional roman math words, or ``log-like"
-functions, to those provided in standard \TeX.  The following
-commands are added: \verb:\const:, \verb:\diag:, \verb:\grad:,
-\verb:\Range:, \verb:\rank:, and \verb:\supp:.
-These commands produce the same word as the command name
-in math mode, in upright type.
-
-\section{Special fonts}
-
-SIAM supports the use of the AMS-\TeX\ fonts (version 2.0
-and later). The package \verb|amsfonts| can be included with
-the command\linebreak \verb|\usepackage{amsfonts}|. This package
-is part of the AMS-\LaTeX distribution, available
-from the AMS or from the Comprehensive TeX Archive
-Network (anonymous ftp to ftp.shsu.edu). The blackboard bold font in this
-font package can be used for designating number sets. 
-This is preferable to other methods of combining letters
-(such as I and R for the real numbers) to produce pseudo-bold
-letters but this is tolerable as well. Typographically speaking,
-number sets may simply be designated using regular bold letters; 
-the blackboard bold typeface was designed to fulfil a desire
-to simulate the limitations of a chalk board in printed type.
-
-
-\subsection{Punctuation}
-All standard punctuation and all numerals should be set in roman type
-(upright) even within italic text. The only exceptions are periods and 
-commas. They may be set to match the surrounding text.
-
-References to sections should use the symbol \S, generated by
-\verb|\S|. (If the reference begins a sentence, the term ``Section''
-should be spelled out in full.) Authors should not redefine
-\verb|\S|, say, to be a calligraphic S, because \verb|\S|
-must be reserved for use as the section symbol.  
-
-Authors sometimes confuse the use of various types of dashes.
-Hyphens (\verb|-|, -) are used for some compound words (many
-such words should have no hyphen but must be run together, 
-like ``nonzero,'' or split apart, like ``well defined''). 
-Minus signs (\verb|$-$|, $-$)
-should be used in math to represent subtraction or negative numbers.
-En dashes (\verb|--|, --) are used for ranges (like 3--5, 
-June--August), or for joined names (like Runge--Kutta). Em dashes
-(\verb|---|, ---) are used to set off a clause---such as this 
-one---from the rest of the sentence. 
-
-
-\subsection{Text formatting}
-
-SIAM style preferences do not make regular use of the \verb|{enumerate}|
-and \verb|{itemize}| environments. Instead,
-{\tt siamltex.cls} includes definitions of two alternate list
-environments, \verb|{remunerate}| and \verb|{romannum}|.
-Unlike the standard itemized lists, these environments do
-not indent the secondary lines of text. The labels, whether
-defaults or the optional user-defined, are always aligned
-flush right.
-
-The \verb|{remunerate}| environment consecutively numbers
-each item with an arabic numeral followed by a period. This
-number is always upright, even in slanted
-environments. (For those wondering at the unusual
-naming of this environment, it comes from Seroul and Levy's
-\cite{SerLev} definition of a similar macro for plain \TeX: 
-%{\tt \char"5C meti} 
-\verb|\meti| which is
-% {\tt \char"5C item}
-\protect\verb|\item|  spelled backwards. Thus
-%{\tt \{remunerate\}}, 
-\verb|{remunerate}|
-a portion of 
-%{\tt \{enumerate\}}
-\verb|{enumerate}|
-spelled backwards.)
-
-The \verb|{romannum}| environment consecutively numbers
-each item with a lower-case roman numeral enclosed in
-parentheses. This number will always be upright within
-slanted environments (as in theorems).
-
-
-\section{Theorems and Lemmas}
-Theorems, lemmas, corollaries, definitions, and propositions are covered
-in the SIAM macros by the theorem-environments
-\verb|{theorem}|, \verb|{lemma}|, \verb|{corollary}|,
-\verb|{definition}| and \verb|{proposition}|. These are all
-numbered in the same sequence and produce labels in small 
-caps with an italic body. Other environments may be specified by the
-\verb|\newtheorem| command. SIAM's style is for Remarks and Examples
-to appear with italic labels and an upright roman body.
-
-\begin{verbatim}
-
-\begin{theorem}
-Sample theorem included for illustration.  
-Numbers and parentheses, like equation $(3.2)$, should be set 
-in roman type.  Note that words (as opposed to ``log-like''
-functions) in displayed equations, such as
-$$ x^2 = Y^2 \sin z^2 \mbox{ for all } x $$
-will appear in italic type in a theorem, though normally
-they should appear in roman.\end{theorem}
-
-\end{verbatim}
-
-This sample produces Theorem 4.1 below.
-
-\begin{theorem}
-Sample theorem included for illustration.  
-Numbers and parentheses, like equation $(3.2)$, should be set 
-in roman type.  Note that words (as opposed to ``log-like''
-functions) in displayed equations, such as
-$$ x^2 = Y^2 \sin z^2 \mbox{ for all } x $$
-will appear in italic type in a theorem, though normally
-they should appear in roman.
-\end{theorem}
-
-
-Proofs are handled with the \verb|\begin{proof}|
-\verb|\end{proof}| environment. A ``QED'' box \endproof\ is created
-automatically by \verb|\end{proof}|, but this should be
-preceded with a \verb|\qquad|.
-
-Named proofs, if used, must be done independently by the
-authors. SIAM style specifies that proofs which end with
-displayed equations should have the QED box two ems (\verb|\qquad|)
-from the end of the equation on line with it horizontally.
-Below is an example of how this can be done:
-
-\begin{verbatim}
-
-{\em Proof}. Proof of the previous theorem 
-                .
-                .
-                .
-thus,
-$$
-a^2 + b^2 = c^2 \qquad\endproof
-$$
-
-\end{verbatim}
-
-
-\section{Figures and tables}
-Figures and tables sometimes require special consideration.
-Tables in SIAM style are need to be set in eight point size
-by using the \verb|\footnotesize| command inside the 
-\verb|\begin{table}| environment. Also, they should be designed 
-so that they do not extend beyond the text margins. 
-
-SIAM style requires that no figures or tables  appear in the
-references section of the paper. \LaTeX\ is notorious for
-making figure placement difficult, so it is important to
-pay particular attention to figure placement near the
-references in the text. All figures and tables should
-be referred to in the text.
-
-SIAM supports the use of {\tt epsfig} for including {\sc PostScript}
-figures. All {\sc Post\-Script} figures should be sent in separate
-files. See the {\tt epsfig} documentation (available via
-anonymous ftp from CTAN: ftp.shsu.edu) for more details on the use
-of this style option. It is a good idea to submit high-quality
-hardcopy of all {\sc Post\-Script} figures just in case there 
-is difficulty in the reproduction of the figure. Figures produced 
-by other non-\TeX\ methods should be included as high-quality 
-hardcopy when  the manuscript is submitted.
-
-{\sc PostScript} figures that are sent should be generated with
-sufficient line thickness. Some past figures authors have sent
-had their line widths become very faint when SIAM set the papers
-using a high-quality 1200dpi printer.
-
-Hardcopy for non-{\sc PostScript} figures should be included in
-the submission of the hardcopy of the manuscript. Space
-should be left in the \verb|{figure}| command for the
-hardcopy to be inserted in production.
-
-\section{Bibliography and Bib\TeX}
-
-If using {\sc Bib}\TeX, authors need not submit the {\tt .bib} file for
-their papers. Merely submit the completed {\tt .bbl} file, having used
-{\tt siam.bst} as their bibliographic style file. {\tt siam.bst}
-only works with Bib\TeX\ version 99i and later. The use of
-Bib\TeX\ and the preparation of a {\tt .bib} file is
-described in greater detail in \cite{Lamport}.
-
-If not using Bib\TeX, SIAM bibliographic references follow
-the format of the following examples:
-
-\begin{verbatim}
-
-\bibitem{Ri} {\sc W. Riter},
-{\em Title of a paper appearing in a book}, in The Book 
-Title, E.~D. One, E.~D. Two, and A.~N. Othereditor, eds., 
-Publisher, Location, 1992, pp.~000--000.
-
-\bibitem{AuTh1} {\sc A.~U. Thorone}, {\em Title of paper
-with lower case letters}, SIAM J. Abbrev. Correctly, 2
-(1992), pp.~000--000.
-
-\bibitem{A1A2} {\sc A.~U. Thorone and A.~U. Thortwo}, {\em
-Title of paper appearing in book}, in Book Title: With All
-Initial Caps, Publisher, Location, 1992.
-
-\bibitem{A1A22} \sameauthor, % generates the 3 em rule
-{\em Title of Book{\rm :} Note Initial Caps and {\rm ROMAN
-TYPE} for Punctuation and Acronyms}, Publisher,
-Location, pp.~000--000, 1992.
-
-\bibitem{AuTh3} {\sc A.~U. Thorthree}, {\em Title of paper
-that's not published yet}, SIAM. J. Abbrev. Correctly, to appear.
-
-\end{verbatim}
-
-Other types of references fall into the same general
-pattern. See the sample file or any SIAM journal for other
-examples. Authors must correctly format their bibliography to
-be considered as having used the macros correctly. An incorrectly 
-formatted bibliography is not only time-consuming for SIAM to
-process but it is possible that errors may be introduced into 
-it by keyboarders/copy editors.
-
-As an alternative to the above style of reference, an alphanumeric
-code may be used in place of the number (e.g., [AUTh90]). The same
-commands are used, but \verb|\bibitem| takes an optional argument
-containing the desired alphanumeric code. 
-
-Another alternative is no number, simply the authors' names and
-the year of publication following in parentheses. The rest of the
-format is identical. The macros do not support this alternative
-directly, but modifications to the macro definition are possible
-if this reference style is preferred.
-
-
-\section{Conclusion} Many other style suggestions and tips
-could be given to help authors but are beyond the scope of this
-document. Simple mistakes can be avoided by increasing your familiarity
-with how \LaTeX\ functions. The books referred to throughout this document
-are also useful to the author who wants clear, beautiful typography
-with minimal mistakes. 
-
-\Appendix
-\section{The use of appendices}
-The \verb|\appendix| command may be used before the final sections
-of a paper to designate them as appendices. Once \verb|\appendix|
-is called, all subsequent sections will appear as 
-
-\appendix
-\section{Title of appendix} Each one will be sequentially lettered
-instead of numbered. Theorem-like environments, subsections,
-and equations will also have the section number changed to a letter.
-
-If there is only {\em one} appendix, however, the \verb|\Appendix|
-(with a capital letter) should be used instead. This produces only 
-the word {\bf Appendix} in the section title, and does not add a letter.
-Equation numbers, theorem numbers and subsections of the appendix
-will have the letter ``A''  designating the section number.
-
-If you don't want to title your appendix, and just call it
-{\bf Appendix A.} for example, use \verb|\appendix\section*{}| 
-and don't include anything in the title field. This works
-opposite to the way \verb|\section*| usually works, by including the
-section number, but not using a title.
-
- 
-Appendices should appear before the bibliography section, not after,
-and any acknowledgments should be placed after the appendices and before
-the bibliography. 
-
-\begin{thebibliography}{1}
-\bibitem{GoMiSa} {\sc M. Goossens, F. Mittelbach, and A. Samarin},
-{\em The} \LaTeX\ {\em Companion}, Addison-Wesley, Reading, MA, 1994.
-
-\bibitem{Higham} {\sc N.~J. Higham}, {\em Handbook of Writing for
-the Mathematical Sciences}, Society for Industrial and Applied
-Mathematics, Philadelphia, PA, 1993.
-
-\bibitem{Lamport} {\sc L. Lamport}, \LaTeX: {\em A Document
-Preparation System}, Addison-Wesley, Reading, MA, 1986.
-
-\bibitem{SerLev} {\sc R. Seroul and S. Levy}, {\em A
-Beginner's Book of} \TeX, Springer-Verlag, Berlin, New
-York, 1991.
-\end{thebibliography}
-
-
-\end{document}
-%% end of file `docultex.tex'
\ No newline at end of file
diff --git a/Master/texmf-dist/doc/latex/siam/lexample.tex b/Master/texmf-dist/doc/latex/siam/lexample.tex
deleted file mode 100644
index a8502d3788a..00000000000
--- a/Master/texmf-dist/doc/latex/siam/lexample.tex
+++ /dev/null
@@ -1,658 +0,0 @@
-%%
-%% This is file `lexample.tex', 
-%% Sample file for siam macros for use with LaTeX 2e
-%% 
-%% By Paul Duggan for the Society for Industrial and Applied
-%% Mathematics. 
-%% 
-%% October 1, 1995
-%%
-%% Version 1.0
-%% 
-%% You are not allowed to change this file. 
-%% 
-%% You are allowed to distribute this file under the condition that 
-%% it is distributed together with all of the files in the siam macro 
-%% distribution. These are:
-%%
-%%  siamltex.cls (main LaTeX macro file for SIAM)
-%%  siamltex.sty (includes siamltex.cls for compatibility mode)
-%%  siam10.clo   (size option for 10pt papers)
-%%  subeqn.clo   (allows equation numbners with lettered subelements)
-%%  siam.bst     (bibliographic style file for BibTeX)
-%%  docultex.tex (documentation file)
-%%  lexample.tex (this file)
-%%
-%% If you receive only some of these files from someone, complain! 
-%% 
-%% You are NOT ALLOWED to distribute this file alone. You are NOT 
-%% ALLOWED to take money for the distribution or use of either this 
-%% file or a changed version, except for a nominal charge for copying 
-%% etc. 
-%% \CharacterTable
-%%  {Upper-case    \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z
-%%   Lower-case    \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z
-%%   Digits        \0\1\2\3\4\5\6\7\8\9
-%%   Exclamation   \!     Double quote  \"     Hash (number) \#
-%%   Dollar        \$     Percent       \%     Ampersand     \&
-%%   Acute accent  \'     Left paren    \(     Right paren   \)
-%%   Asterisk      \*     Plus          \+     Comma         \,
-%%   Minus         \-     Point         \.     Solidus       \/
-%%   Colon         \:     Semicolon     \;     Less than     \<
-%%   Equals        \=     Greater than  \>     Question mark \?
-%%   Commercial at \@     Left bracket  \[     Backslash     \\
-%%   Right bracket \]     Circumflex    \^     Underscore    \_
-%%   Grave accent  \`     Left brace    \{     Vertical bar  \|
-%%   Right brace   \}     Tilde         \~}
-
-
-\documentclass[final]{siamltex}
-
-% definitions used by included articles, reproduced here for 
-% educational benefit, and to minimize alterations needed to be made
-% in developing this sample file.
-
-\newcommand{\pe}{\psi}
-\def\d{\delta} 
-\def\ds{\displaystyle} 
-\def\e{{\epsilon}} 
-\def\eb{\bar{\eta}}  
-\def\enorm#1{\|#1\|_2} 
-\def\Fp{F^\prime}  
-\def\fishpack{{FISHPACK}} 
-\def\fortran{{FORTRAN}} 
-\def\gmres{{GMRES}} 
-\def\gmresm{{\rm GMRES($m$)}} 
-\def\Kc{{\cal K}} 
-\def\norm#1{\|#1\|} 
-\def\wb{{\bar w}} 
-\def\zb{{\bar z}} 
-
-% some definitions of bold math italics to make typing easier.
-% They are used in the corollary.
-
-\def\bfE{\mbox{\boldmath$E$}}
-\def\bfG{\mbox{\boldmath$G$}}
-
-\title{Sample file for SIAM \LaTeX\ macro package\thanks{This 
-        work was supported by the Society for Industrial and
-        Applied Mathematics, Philadelphia, Pennsylvania.}}
-
-% The thanks line in the title should be filled in if there is
-% any support acknowledgement for the overall work to be included
-% This \thanks is also used for the received by date info, but
-% authors are not expected to provide this.
-
-\author{Paul Duggan\thanks{Composition Department, Society
-        for Industrial and Applied Mathematics, 3600 Univeristy 
-        City Science Center, Philadelphia, Pennsylvania, 
-        19104-2688 ({\tt duggan@siam.org}).}
-        \and Various A.~U. Thors\thanks{Various Affiliations, 
-        supported by various foundation grants.}}
-
-\begin{document}
-
-\maketitle
-
-\begin{abstract}
-An example of SIAM \LaTeX\ macros is presented. Various
-aspects of composing manuscripts for SIAM's journal series
-are illustrated with actual examples from accepted
-manuscripts. SIAM's stylistic standards are adhered to
-throughout, and illustrated.
-\end{abstract}
-
-\begin{keywords} 
-sign-nonsingular matrix, LU-factorization, indicator
-polynomial 
-\end{keywords}
-
-\begin{AMS}
-15A15, 15A09, 15A23
-\end{AMS}
-
-\pagestyle{myheadings}
-\thispagestyle{plain}
-\markboth{P. DUGGAN AND V. A. U. THORS}{SIAM MACRO EXAMPLES}
-
-
-\section{Introduction and examples}
-This paper presents a sample file for the use of SIAM's
-\LaTeX\ macro package. It illustrates the features of the
-macro package, using actual examples culled from various
-papers published in SIAM's journals. It is to be expected
-that this sample will provide examples of how to use the
-macros to generate standard elements of journal papers,
-e.g., theorems, definitions, or figures. This paper also
-serves as an example of SIAM's stylistic preferences for
-the formatting of such elements as bibliographic references,
-displayed equations, and equation arrays, among others.
-Some special circumstances are not dealt with in this
-sample file; for such information one should see the
-included documentation file.
-
-{\em Note:} This paper is not to be read in any form for content. 
-The conglomeration of equations, lemmas, and other text elements were 
-put together solely for typographic illustrative purposes and don't 
-make any sense as lemmas, equations, etc.
-
-\subsection{Sample text}
-Let $S=[s_{ij}]$ ($1\leq i,j\leq n$) be a $(0,1,-1)$-matrix
-of order $n$. Then $S$ is a {\em sign-nonsingular matrix}
-(SNS-matrix) provided that each real matrix with the same
-sign pattern as $S$ is nonsingular. There has been
-considerable recent interest in constructing and
-characterizing SNS-matrices \cite{bs}, \cite{klm}. There
-has also been interest in strong forms of
-sign-nonsingularity \cite{djd}. In this paper we give a new
-generalization of SNS-matrices and investigate some of
-their basic properties.
- 
-Let $S=[s_{ij}]$ be a $(0,1,-1)$-matrix of order $n$ and
-let $C=[c_{ij}]$ be a real matrix of order $n$. The pair
-$(S,C)$ is called a {\em matrix pair of order} $n$.
-Throughout, $X=[x_{ij}]$ denotes a matrix of order $n$
-whose entries are algebraically independent indeterminates
-over the real field. Let $S\circ X$ denote the Hadamard
-product (entrywise product) of $S$ and $X$. We say that the
-pair $(S,C)$ is a {\em sign-nonsingular matrix pair of
-order} $n$, abbreviated SNS-{\em matrix pair of order} $n$,
-provided that the matrix \[A=S\circ X+C\] is nonsingular
-for all positive real values of the $x_{ij}$.  If $C=O$
-then the pair $(S,O)$ is a SNS-matrix pair if and only if
-$S$ is a SNS-matrix.  If $S=O$ then the pair $(O,C)$ is a
-SNS-matrix pair if and only if $C$ is nonsingular. Thus
-SNS-matrix pairs include both nonsingular matrices and
-sign-nonsingular matrices as special cases.
- 
-The pairs $(S,C)$ with
-\[S=\left[\begin{array}{cc}1&0\\0&0\end{array}\right],\qquad 
-C=\left[\begin{array}{cc}1&1\\1&1\end{array}\right]\] and 
-\[S=\left[\begin{array}{ccc}1&1&0\\1&1&0\\0&0&0\end{array}\right],\qquad 
-C=\left[\begin{array}{ccc}0&0&1\\0&2&0\\
-3&0&0\end{array}\right]\] are examples of SNS-matrix pairs.
-
-\subsection{A remuneration list}
-In this paper we consider the evaluation of integrals of the 
-following forms:
-\begin{equation}
-\int_a^b \left( \sum_i E_i B_{i,k,x}(t) \right)
-         \left( \sum_j F_j B_{j,l,y}(t) \right) dt,\label{problem}
-\end{equation}
-\begin{equation}
-\int_a^b f(t) \left( \sum_i E_i B_{i,k,x}(t) \right) dt,\label{problem2}
-\end{equation}
-where $B_{i,k,x}$ is the $i$th B-spline of order $k$ defined over the
-knots $x_i, x_{i+1}, \ldots, x_{i+k}$.
-We will consider B-splines normalized so that their integral is one.
-The splines may be of different orders and
-defined on different knot sequences $x$ and $y$.
-Often the limits of integration will be the entire real line, $-\infty$
-to $+\infty$. Note that (\ref{problem}) is a special case of (\ref{problem2})
-where $f(t)$ is a spline.
-
-
-There are five different methods for calculating (\ref{problem})
-that will be considered:
-\begin{remunerate}
-\item Use Gauss quadrature on each interval.
-\item Convert the integral to a linear combination of
-      integrals of products of B-splines and provide a recurrence for
-      integrating the product of a pair of B-splines.
-\item Convert the sums of B-splines to piecewise
-      B\'{e}zier format and integrate segment
-      by segment using the properties of the Bernstein polynomials.
-\item Express the product of a pair of B-splines as a linear combination
-      of B-splines.
-      Use this to reformulate the integrand as a linear combination
-      of B-splines, and integrate term by term.
-\item Integrate by parts.
-\end{remunerate}
-Of these five, only methods 1 and 5 are suitable for calculating 
-(\ref{problem2}). The first four methods will be touched on and the 
-last will be discussed at length.
-
-
-\subsection{Some displayed equations and \{{\tt eqnarray}\}s}
-     By introducing the product topology on  $R^{m \times m} \times
-R^{n \times n}$  with the induced inner product
-\begin{equation}
-\langle (A_{1},B_{1}), (A_{2},B_{2})\rangle := \langle A_{1},A_{2}\rangle 
-+ \langle B_{1},B_{2}\rangle,\label{eq2.10}
-\end{equation}
-we calculate the Fr\'{e}chet derivative of  $F$  as follows:
-\begin{eqnarray}
- F'(U,V)(H,K) &=& \langle R(U,V),H\Sigma V^{T} + U\Sigma K^{T} -
-P(H\Sigma V^{T} + U\Sigma K^{T})\rangle \nonumber \\
-         &=& \langle R(U,V),H\Sigma V^{T} + U\Sigma K^{T}\rangle \label{eq2.11} \\
-&=& \langle R(U,V)V\Sigma^{T},H\rangle + \langle \Sigma^{T}U^{T}R(U,V),K^{T}\rangle.     \nonumber
-\end{eqnarray}
-In the middle line of (\ref{eq2.11}) we have used the fact that the range of
-$R$ is always perpendicular to the range of $P$.  The gradient $\nabla F$  of
-$F$, therefore,  may be interpreted as the
-pair of matrices:
-\begin{equation}
- \nabla F(U,V) = (R(U,V)V\Sigma^{T},R(U,V)^{T}U\Sigma ) \in
-R^{m \times m} \times R^{n \times n}.       			\label{eq2.12}
-\end{equation}
-Because of the product topology, we know
-\begin{equation}
- {\cal T}_{(U,V)}({\cal O} (m) \times {\cal O} (n)) =
-{\cal T}_{U}{\cal O} (m) \times {\cal T}_{V}{\cal O} (n),  		\label{eq2.13}
-\end{equation}
-where  ${\cal T}_{(U,V)}({\cal O} (m) \times {\cal O} (n))$  stands for the
-tangent space to the manifold  ${\cal O} (m) \times {\cal O} (n)$  at  $(U,V)
-\in {\cal O} (m) \times {\cal O} (n)$  and so on.  The projection of
-$\nabla F(U,V)$  onto  ${\cal T}_{(U,V)}({\cal O} (m) \times {\cal O} (n))$,
-therefore, is the product of the projection of the first component of
-$\nabla F(U,V)$  onto  ${\cal T}_{U}{\cal O} (m)$  and the projection of the
-second component of  $\nabla F(U,V)$  onto  ${\cal T}_{V}{\cal O} (n)$. 
-In particular, we claim that the
-projection $ g(U,V)$  of the gradient  $\nabla F(U,V)$  onto
-${\cal T}_{(U,V)}({\cal O} (m) \times {\cal O} (n))$  is given by the pair of
-matrices:
-\begin{eqnarray}
-g(U,V) = && \left( \frac{R(U,V)V\Sigma^{T}U^{T}-U\Sigma V^{T}R(U,V)^{T}}{2}U,
-\right.			\nonumber \\[-1.5ex]
-\label{eq2.14}\\[-1.5ex]
-&&\quad \left. \frac{R(U,V)^{T}U\Sigma V^{T}-V
-   \Sigma^{T}U^{T}R(U,V)}{2}V \right).\nonumber
-\end{eqnarray}
-Thus, the vector field
-\begin{equation}
-\frac{d(U,V)}{dt} = -g(U,V) 	\label{eq2.15}
-\end{equation}
-defines a steepest descent flow on the manifold  ${\cal O} (m) \times
-{\cal O} (n)$ for the objective function  $F(U,V)$.
-
- 
-\section{Main results} 
- 
-Let $(S,C)$ be a matrix pair of order $n$.  The determinant
-\[\det (S\circ X+C)\] 
-is a polynomial in the indeterminates of $X$ of degree at
-most $n$ over the real field. We call this polynomial the
-{\em indicator polynomial} of the matrix pair $(S,C)$
-because of the following proposition.
- 
-\begin{theorem} 
-\label{th:prop} 
-The matrix pair $(S,C)$ is a {\rm SNS}-matrix pair if and
-only if all the nonzero coefficients in its indicator
-polynomial have the same sign and there is at least one
-nonzero coefficient.
-\end{theorem} 
- 
-\begin{proof}
-Assume that $(S,C)$ is a SNS-matrix pair.  Clearly the
-indicator polynomial has a nonzero coefficient.  Consider a
-monomial
-\begin{equation} 
-\label{eq:mono} 
-b_{i_{1},\ldots,i_{k};j_{1},\ldots,j_{k}}x_{i_{1}j_{1}}\cdots
-x_{i_{k}j_{k}}
-\end{equation} 
-occurring in the indicator polynomial with a nonzero
-coefficient.  By taking the $x_{ij}$ that occur in
-(\ref{eq:mono}) large and all others small, we see that any
-monomial that occurs in the indicator polynomial with a
-nonzero coefficient can be made to dominate all others.
-Hence all the nonzero coefficients have the same sign. The
-converse is im-\linebreak mediate. \qquad\end{proof} 
- 
-
-For SNS-matrix pairs $(S,C)$ with $C=O$ the indicator
-polynomial is a homogeneous polynomial of degree $n$. In
-this case Theorem \ref{th:prop} is a standard fact about
-SNS-matrices.
- 
-\begin{lemma}[{\rm Stability}]
-\label{stability}
-Given $T>0$, suppose that $\| \epsilon (t) \|_{1,2} \leq h^{q-2}$
-for $0 \leq t \leq T$ and $q \geq 6$. 
-Then there exists a positive number $B$ that depends on
-$T$ and the exact solution $\pe$ only such that for all $0 \leq t \leq T$,
-\begin{equation}
-\label{Gron}
-\frac {d}{dt} \| \epsilon (t) \| _{1,2}  \leq B
-   ( h^{q-3/2} + \| \epsilon (t) \|_{1,2})\;.
-\end{equation}
-The function $B(T)$ can be chosen to be nondecreasing in time.
-\end{lemma}
- 
- 
-\begin{theorem} 
-\label{th:gibson} 
-The maximum number of nonzero entries in a {\rm SNS}-matrix
-$S$ of order $n$ equals \[\frac{n^{2}+3n-2}{2}\] with
-equality if and only if there exist permutation matrices
-such that $P|S|Q=T_{n}$ where
-\begin{equation} 
-\label{eq:gibson} 
-T_{n}=\left[\begin{array}{cccccc} 1&1&\cdots&1&1&1\\
-1&1&\cdots&1&1&1\\ 0&1&\cdots&1&1&1\\ 
-\vdots&\vdots&\ddots&\vdots&\vdots&\vdots\\ 
-0&0&\cdots&1&1&1\\ 0&0&\cdots&0&1&1\end{array}\right]. 
-\end{equation} 
-\end{theorem} 
- 
-We note for later use that each submatrix of $T_{n}$ of
-order $n-1$ has all 1s on its main diagonal. 
- 
-We now obtain a bound on the number of nonzero entries of
-$S$ in a SNS-matrix pair $(S,C)$ in terms of the degree of
-the indicator polynomial. We denote the strictly upper
-triangular (0,1)-matrix of order $m$ with all 1s above the
-main diagonal by $U_{m}$. The all 1s matrix of size $m$ by
-$p$ is denoted by $J_{m,p}$.
- 
- 
-\begin{proposition}[{\rm Convolution theorem}]
-\label{pro:2.1}  Let
-\begin{eqnarray*}
-a\ast u(t) = \int_0^t a(t- \tau) u(\tau) d\tau, \hspace{.2in} t \in
-(0, \infty).
-\end{eqnarray*}
-Then
-\begin{eqnarray*}
-\widehat{a\ast u}(s) = \widehat{a}(s)\widehat{u}(s).
-\end{eqnarray*}
-\end{proposition}
-
-\begin{lemma}
-\label{lem:3.1}
-For $s_0 >0$, if
-$$
-\int_0^{\infty} e^{-2s_0 t}v^{(1)}(t) v(t) dt \; \leq 0 \;,
-$$
-then
-\begin{eqnarray*}
-\int_0^{\infty} e^{-2s_0 t} v^2(t) dt \; \leq \; \frac{1}{2s_0} v^2(0).
-\end{eqnarray*}
-\end{lemma}
-
-{\em Proof}. Applying integration by parts, we obtain
-\begin{eqnarray*}
-\int_0^{\infty} e^{-2s_0 t} [v^2(t)-v^2(0)] dt
-&=&\lim_{t\rightarrow \infty}\left (
--\frac{1}{2s_0}e^{-2s_0 t}v^2(t) \right ) +\frac{1}{s_0}
-\int_0^{\infty} e^{-2s_0 t}v^{(1)}(t)v(t)dt\\
-&\leq& \frac{1}{s_0} \int_0^{\infty} e^{-2s_0 t} v^{(1)}(t)v(t) dt \;\;
-\leq \;\; 0.
-\end{eqnarray*}
-Thus
-$$
-\int_0^{\infty} e^{-2s_0 t} v^2(t) dt \;\;\leq v^2(0) \int_0^{\infty}
-\;\;e^{-2s_0 t} dt\;\;=\;\;\frac{1}{2s_0} v^2(0).\eqno\endproof
-$$
-
-\begin{corollary}\label{c4.1}
-Let $ \bfE $ satisfy $(5)$--$(6)$ and
-suppose $ \bfE^h $ satisfies $(7)$ and $(8)$
-with a general $ \bfG $.  Let $ \bfG= \nabla \times {\bf \Phi} + \nabla p,$
-$p \in H_0^1 (\Omega) $. Suppose that $\nabla p$ and $ \nabla \times 
-{\bf \Phi} $ satisfy all the assumptions of Theorems $4.1$ and  
-$4.2$, respectively. In addition suppose all the regularity
-assumptions of Theorems $4.1$--$4.2$ are satisfied.  Then 
-for $ 0 \le t \le T $ and $ 0 < \epsilon \le \epsilon_0 $ there exists a 
-constant $ C = C(\epsilon, T) $ such that
-$$
-\Vert (\bfE - \bfE^h)(t) \Vert_0 \le C h^{k+1- \epsilon},
-$$
-where $ C $ also depends on the constants given in Theorems 
-$4.1$ and $4.2$.
-\end{corollary}
-
-
-\begin{definition}
-Let $S$ be an isolated invariant set with isolating neighborhood $N$.
-An {\em index pair} for $S$ is a pair of compact sets $(N_{1},N_{0})$
-with $N_{0} \subset N_{1} \subset N$ such that:
-\begin{romannum}
-\item $cl(N_{1} \backslash N_{0})$
-is an isolating neighborhood for $S$.
-\item $N_{i}$ is positively invariant relative to $N$ for $i=0,1$,
-i.e., given
-$x \in N_{i}$ and $x \cdot [0,t] \subset N$, then $x \cdot [0,t] \subset
-N_{i}$.
-\item $N_{0}$ is an exit set for $N_{1}$, i.e. if $x \in N_{1}$,
-$x \cdot [0, \infty ) \not\subset N_{1}$, then there is a $T \geq 0$ such
-that $x \cdot [0,T] \subset N_{1}$ and $x \cdot T \in N_{0}$.
-\end{romannum}
-\end{definition}
-
-\subsection{Numerical experiments} We conducted numerical experiments 
-in computing inexact Newton steps for discretizations of a  
-{\em modified Bratu problem}, given by  
-\begin{eqnarray} 
-{\ds \Delta w + c e^w + d{ {\partial w}\over{\partial x} } } 
-&=&{\ds f \quad {\rm in}\ D, }\nonumber\\[-1.5ex]
-\label{bratu} \\[-1.5ex]
-{\ds w }&=&{\ds 0 \quad {\rm on}\ \partial D , } \nonumber
-\end{eqnarray} 
-where $c$ and $d$ are constants. The actual Bratu problem has $d=0$ and  
-$f \equiv0$. It provides a simplified model of nonlinear diffusion  
-phenomena, e.g., in combustion and semiconductors, and has been 
-considered by Glowinski, Keller, and Rheinhardt \cite{GloKR85}, 
-as well as by a number of other investigators; see \cite{GloKR85} 
-and the references therein. See also problem 3 by Glowinski and  Keller  
-and problem 7 by Mittelmann in the collection of nonlinear model 
-problems assembled by Mor\'e \cite{More}. The modified problem  
-(\ref{bratu}) has been used as a test problem for inexact Newton 
-methods by Brown and Saad \cite{Brown-Saad1}.  
- 
-In our experiments, we took $D = [0,1]\times[0,1]$, $f \equiv0$, 
-$c=d=10$, and discretized (\ref{bratu}) using the usual second-order 
-centered differences over a $100\times100$ mesh of equally 
-spaced points in $D$. In \gmres($m$), we took $m=10$ and used fast  
-Poisson right preconditioning as in the experiments in \S2. The computing  
-environment was as described in \S2. All computing was done  
-in double precision.  
- 
- 
-
-\begin{figure}[ht] 
-\vspace{2.5in}
-\caption{{\rm Log}$_{10}$ of the residual norm versus the number of
-{\rm GMRES$(m)$} iterations for the finite difference methods.} 
-\label{diff} 
-\end{figure}  
- 
-
- 
-In the first set of experiments, we allowed each method to  
-run for $40$ {\gmresm} iterations, starting with zero as the initial  
-approximate solution, after which the limit of residual norm  
-reduction had been reached. The results are shown in Fig.~\ref{diff}.  
-In Fig.~\ref{diff}, the top curve was produced by method FD1. 
-The second curve from the top is actually a superposition of  
-the curves produced by methods EHA2 and FD2; the two curves are 
-visually indistinguishable. Similarly, the third curve from  
-the top is a superposition of the curves produced by methods EHA4 
-and FD4, and the fourth curve from the top, which lies barely above  
-the bottom curve, is a superposition of the curves produced by  
-methods EHA6 and FD6. The bottom curve was produced by method A. 
- 
-In the second set of experiments, our purpose was to assess the 
-relative amount of computational work required by the methods  
-which use higher-order differencing to reach comparable levels  
-of residual norm reduction. We compared pairs of methods EHA2  
-and FD2, EHA4 and FD4, and EHA6 and FD6 by observing in each of 
-20 trials the number of {\gmresm} iterations, number of $F$-evaluations,  
-and run time required by each method to reduce the residual norm 
-by a factor of $\e$, where for each pair of methods $\e$ was chosen  
-to be somewhat greater than the limiting ratio of final to  
-initial residual norms obtainable by the methods. In these trials,  
-the initial approximate solutions were obtained by generating random  
-components as in the similar experiments in \S2. We note that for every  
-method, the numbers of {\gmresm} iterations and $F$-evaluations required  
-before termination did not vary at all over the 20 trials. The {\gmresm}
-iteration counts, numbers of $F$-evaluations, and means and standard  
-deviations of the run times are given in Table \ref{diffstats}. 
- 
-\begin{table}
-\caption{Statistics over $20$ trials of {\rm GMRES$(m)$} iteration numbers,  
-$F$-evaluations, and run times required to reduce the residual norm by  
-a factor of $\e$. For each method, the number of {\rm GMRES$(m)$} iterations  
-and $F$-evaluations was the same in every trial.} 
-
-\begin{center} \footnotesize
-\begin{tabular}{|c|c|c|c|c|c|} \hline  
-&& Number of & Number of & Mean Run Time & Standard \\ 
-Method & $\e$ & Iterations & $F$-Evaluations& (Seconds) & Deviation \\ \hline 
-\lower.3ex\hbox{EHA2} & \lower.3ex\hbox{$10^{-10}$} & \lower.3ex\hbox{26} &  
-\lower.3ex\hbox{32} & \lower.3ex\hbox{47.12} & \lower.3ex\hbox{.1048} \\ 
-FD2 & $10^{-10}$ & 26 & 58 & 53.79 & .1829 \\ \hline  
-\lower.3ex\hbox{EHA4} & \lower.3ex\hbox{$10^{-12}$} & \lower.3ex\hbox{30} &  
-\lower.3ex\hbox{42} & \lower.3ex\hbox{56.76} & \lower.3ex\hbox{.1855} \\  
-FD4 & $10^{-12}$ & 30 & 132 & 81.35 & .3730 \\ \hline  
-\lower.3ex\hbox{EHA6} & \lower.3ex\hbox{$10^{-12}$} & \lower.3ex\hbox{30} &  
-\lower.3ex\hbox{48} & \lower.3ex\hbox{58.56} & \lower.3ex\hbox{.1952} \\ 
-FD6 & $10^{-12}$ & 30 & 198 & 100.6 & .3278 \\ \hline  
-\end{tabular}
-\end{center} 
-\label{diffstats} 
-\end{table}  
-
-In our first set of experiments, we took $c=d=10$ and used right 
-preconditioning with a fast Poisson solver from {\fishpack}  
-\cite{Swarztrauber-Sweet}, which is very effective for these  
-fairly small values of $c$ and $d$. We first started each method 
-with zero as the initial approximate solution and allowed it  
-to run for 40 {\gmresm} iterations, after which the limit of residual  
-norm reduction had been reached. Figure \ref{pdep} shows plots  
-of the logarithm of the Euclidean norm of the residual versus  
-the number of {\gmresm} iterations for the three methods. We note
-that in  Fig.~\ref{pdep} and in all other figures below, the plotted
-residual norms were not the values maintained by {\gmresm}, but rather
-were computed as accurately as possible ``from scratch.''  That is, 
-at each {\gmresm} iteration, the current approximate solution was 
-formed and its product with the coefficient matrix was subtracted 
-from the right-hand side, all in double precision.  
-It was important to compute the residual norms in this way because  
-the values maintained by {\gmresm} become increasingly untrustworthy  
-as the limits of residual norm reduction are neared; see \cite{Walker88}.  
-It is seen in Fig.~\ref{pdep} that Algorithm EHA achieved  
-the same ultimate level of residual norm reduction as the FDP  
-method and required only a few more {\gmresm} iterations to do
-so.  
- 
-\begin{figure}[t] 
-\vspace{3in}
-\caption{{\rm Log}$_{10}$ of the residual norm versus the number of 
-{\rm GMRES}$(m)$ iterations for $c=d=10$ with fast Poisson
-preconditioning. Solid curve: Algorithm {\rm EHA}; dotted 
-curve: {\rm FDP} method; dashed curve: {\rm FSP} method.} 
-\label{pdep} 
-\end{figure} 
- 
- 
-In our second set of experiments, we took $c=d=100$ and carried out  
-trials analogous to those in the first set above. No preconditioning  
-was used in these experiments, both because we wanted to compare 
-the methods without preconditioning and because the fast  
-Poisson preconditioning used in the first set of experiments is 
-not cost effective for these large values of $c$ and $d$. We first  
-allowed each method to run for 600 {\gmresm} iterations, 
-starting with zero as the initial approximate solution, after which  
-the limit of residual norm reduction had been reached. 
- 
-
-\section*{Acknowledgments}
-The author thanks the anonymous authors whose work largely
-constitutes this sample file. He also thanks the INFO-TeX mailing
-list for the valuable indirect assistance he received.
- 
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-\end{document} 
-