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authorKarl Berry <karl@freefriends.org>2007-01-10 22:24:14 +0000
committerKarl Berry <karl@freefriends.org>2007-01-10 22:24:14 +0000
commit8a88f72a120a3d7f214cf0c24916e0c24da2a130 (patch)
tree47882be5f5f0fe051b894d8db556833a1f05f718 /Master/texmf-dist/source
parentde0d34e2013ef10d645ab355c2a7f53510fc171c (diff)
remove siam, selling not allowed
git-svn-id: svn://tug.org/texlive/trunk@3310 c570f23f-e606-0410-a88d-b1316a301751
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-rw-r--r--Master/texmf-dist/source/latex/siam/ltexconf.all112
-rw-r--r--Master/texmf-dist/source/latex/siam/ltexnec.all1923
-rw-r--r--Master/texmf-dist/source/latex/siam/ltexpprt.all702
-rw-r--r--Master/texmf-dist/source/latex/siam/ltexproc.all1784
-rw-r--r--Master/texmf-dist/source/latex/siam/ptexconf.all102
-rw-r--r--Master/texmf-dist/source/latex/siam/ptexnec.all707
-rw-r--r--Master/texmf-dist/source/latex/siam/ptexpprt.all724
-rw-r--r--Master/texmf-dist/source/latex/siam/ptexproc.all704
-rw-r--r--Master/texmf-dist/source/latex/siam/soda209.all682
-rw-r--r--Master/texmf-dist/source/latex/siam/soda2e.all688
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diff --git a/Master/texmf-dist/source/latex/siam/ltexconf.all b/Master/texmf-dist/source/latex/siam/ltexconf.all
deleted file mode 100644
index 2e4a638f423..00000000000
--- a/Master/texmf-dist/source/latex/siam/ltexconf.all
+++ /dev/null
@@ -1,112 +0,0 @@
-
-Please answer the following:
-
-1. Name of conference
-
-2. Type of Presentation
- Contributed: Lecture form
- Poster form
- Minisymposium:
-
-3. Equipment for Visual Support
- Lecture Form/Minisymposium:
- Overhead Projector
- 2" x 2" Slide Projector (35mm)
- Poster Form:
- Easel Poster Board
- Other (specify)
-
-More sophisticated equipment can be provided, but you may be
-required to pay the rental fee. For details, indicate your
-requirements below:
-
-
-4. If you are a speaker in a minisymposium, who is the organizer?
-
-5. What is the minisymposium title?
-
-6. If more than one author, who will present the paper?
-
-% This is a macro file for creating a SIAM Conference abstract in
-% LaTeX.
-%
-% If you have any questions regarding these macros contact:
-% Lillian Hunt
-% SIAM
-% 3600 University City Center Center
-% Philadelphia, PA 19104-2688
-% USA
-% (215) 382-9800
-% e-mail:meetings@siam.org
-
-
-\hsize=25.5pc
-\vsize=50pc
-\textheight 50pc
-\textwidth 25.5pc
-\parskip 0pt
-\parindent 0pt
-\pagestyle{plain}
-
-\def\title#1{\bf{#1}\vspace{6pt}}
-\def\abstract#1{\rm {#1}\vspace{6pt}}
-\def\author#1{\rm {#1}\vfill\eject}
-
-% end of style file
-
-% This is ltexconf.tex. Use this file as an example file for doing an SIAM
-% Conference abstract in LaTeX.
-
-
-\documentstyle[ltexconf]{report}
-\begin{document}
-
-\title{Numerical Analysis of a 1-Dimensional
-Immersed-Boundary\\ Method}
-
-\abstract{We present the numerical analysis of a simplified,
-one-dimensional version
-of Peskin's immersed boundary method, which has been used to
-solve
-the two- and three-dimensional Navier-Stokes equations in the
-presence of immersed boundaries. We consider the heat
-equation
- in a finite domain with a moving source term.
-We denote the solution as $u(x,t)$ and the location of the
-source
- term as $X(t)$. The source term is a moving delta function
-whose strength is a function of u at the location of the
-delta function.
-The p.d.e. is coupled to an ordinary differential equation
-whose
-solution gives the location of the source term.
- The o.d.e. is $X'(t) = u(X(t),t)$, which can be interpreted as
-saying the source term moves at the local velocity.
-The accuracy the numerical method of solution depends on how
-the
-delta function is discretized when the delta function is not
-at
-a grid point and on how the solution, u, is represented
- at locations between grid points. We present results showing
-the effect of different choices of spreading the source to
-the grid and
-of restricting the solution to the source location.
-The problem we analyze is also similar to the Stefan problem
-and
-the immersed-boundary method has features in common with
-particle-in-cell
- methods.}
- \author{\underbar{Richard P. Beyer, Jr.}\\
-University of Washington, Seattle, WA\\
-Randall J. LeVeque\\
-University of Washington, Seattle, WA}
-
-\end{document}
-
-% end of example file.
-
-
-
-Please furnish complete addresses all co-authors.
-
-PLEASE INDICATE WHAT CONFERENCE ABSTRACT IS FOR.
diff --git a/Master/texmf-dist/source/latex/siam/ltexnec.all b/Master/texmf-dist/source/latex/siam/ltexnec.all
deleted file mode 100644
index 9b22936a18c..00000000000
--- a/Master/texmf-dist/source/latex/siam/ltexnec.all
+++ /dev/null
@@ -1,1923 +0,0 @@
-
-This file (ltexnec.all) constitutes the full distribution for NEC Proceedings
-Series LaTeX version macros. The files included here are:
-
-ltexnec.tex (An example file, also containing documentation)
-
-ltexnec.sty (The style file)
-
-siamproc.bst (for BiBTeX users)
-
-To use these macros, separate the files at the indicated cut lines.
-
-%%%%%%%%%%%%%%%%%%%%%%%%CUT HERE%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-
-% This is ltexnec.tex, an example file for use with the NEC
-% Proceedings Series macros.
-% Please take the time to read the following comments, as they describe
-% how to use these macros. This file can be composed and printed out for
-% use as sample output.
-
-% Any comments or questions regarding these macros should be directed to:
-%
-% Corey Gray
-% SIAM
-% 3600 University City Science Center
-% Philadelphia, PA 19104-2688
-% USA
-% Telephone: (215) 382-9800
-% Fax: (215) 386-7999
-% e-mail: gray@siam.org
-
-
-% This file is to be used as an example for style only. It should not be read
-% for content.
-
-%%%%%%%%%%%%%%% PLEASE NOTE THE FOLLOWING STYLE RESTRICTIONS %%%%%%%%%%%%%%%
-
-%% 1. There are no new tags. Existing LaTeX tags have been formatted to
-%% match the Proceedings series style.
-%%
-%% 2. You must use \cite in the text to mark your reference citations and
-%% \bibitem in the listing of references at the end of your chapter. See
-%% the examples in the following file. The file siam.bst has been
-%% included for use with BiBTeX. Please be sure to include the appropriate
-%% .bib file with BiBTeX submissions. You may also submit the .bbl file
-%% instead of the .bib file.
-%%
-%% 3. Unless otherwise stated by your editor, do your chapter as if it
-%% is Chapter 1. The appropriate chapter number will be included during
-%% the production of the proceedings.
-%%
-%% 4. This macro is set up for three levels of headings (\section,
-%% \subsection, and \subsubsection). The macro will automatically number
-%% the headings for you.
-%%
-%% 5. The running heads are indicated by the \markboth command. Please
-%% define the running heads by placing the authors last names in the
-%% first field and the title of the paper in the second field.
-%% They should be typed initial cap and lower case. Please see the example.
-%% Neither field can contain more than 50 characters including spaces,
-%% so please use a shortened version of the title if necessary. For
-%% papers with multiple authors please follow these rules; for
-%% two authors type {Author 1 and Author 2}; for more that two authors type
-%% {Author 1 et al.}.
-%%
-%% 6. Theorems, Lemmas, Definitions, etc. are to be double-numbered,
-%% indicating the section and the occurrence of that element
-%% within that section. (For example, the first theorem in the second
-%% section would be numbered 2.1. The macro will
-%% automatically do the numbering for you.
-%%
-%% 7. Proofs are handled with the commands \begin{proof}\end{proof}.
-%% If you wish to use an end of proof box, use \qed preceding \end{proof}.
-%% The example uses one. It is not required.
-%%
-%% 8. Figures, equations, and tables must be single-numbered. All equation
-%% numbers are to be on the left. Figure captions should be placed under
-%% the figures they pertain to. Table captions should be placed above
-%% the tables. Use existing LaTeX tags for these elements. Numbering of
-%% these elements will be done automatically. SIAM supports the use of
-%% psfig for including Postscript figures. All Postscript figures should be
-%% sent as separate files. A hardcopy version of all Postscript figures
-%% is also required. See note regarding this under How to Submit Your Paper.
-%%
-%% 9. Grant information and author affiliations.
-%% This information is included in the file with the two commands,
-%% \thanks and \footnotemark []. (See example). The \thanks command
-%% produces a footnote for the title or author, and places the
-%% appropriate footnote symbol with the title or author and at the
-%% bottom of the page. The \footnotemark [] command allows the use of
-%% duplicate footnote symbols. This macro follows the normal LaTeX order
-%% of footnote symbols. Below is a list of these symbols, and their
-%% corresponding footnotemark:
-%%
-%% asterisk \footnotemark[1]
-%% single-dagger \footnotemark[2]
-%% double-dagger \footnotemark[3]
-%% section sign \footnotemark[4]
-%% paragraph \footnotemark[5]
-%% parallel \footnotemark[6]
-%% double asterisk \footnotemark[7]
-%% double single-dagger \footnotemark[8]
-%% double double-dagger \footnotemark[9]
-%%
-%% The following general rules for grants and affiliations apply:
-%% a) If there is a single grant for the paper, then the grant
-%% information should be footnoted to the title.
-%% b) If there is more than one grant, include the grant information
-%% with each author's affiliation.
-%% c) If there are different grants for the paper but the authors share
-%% the same affiliation, footnote the grant information to the title.
-%% For example, The work of the first author was supported by xyz.
-%% The work of the second author was supported by abc. And so on.
-%% d) For authors sharing the same affiliation, use \thanks for the
-%% first author with that affiliation and the appropriate
-%% \footnotemark[] (from the list above) for all subsequent authors
-%% with that affiliation.
-%%
-%% 10. Special fonts.
-%% SIAM supports the use of AMS-TeX fonts version 2.0 and later. As
-%% described in the manual for these fonts, they can be included by
-%% \input{amssym.def} and \input{amssym.tex}. These macros are not yet
-%% updated to make use of the New Font Selection Scheme (NFSS) of
-%% Mittelbach and Schopf. To make these macros compatible with NFSS, use
-%% the oldlfont style option.
-%%
-%% 11. How to Submit Your Paper.
-%% The electronic version of your paper should be sent to proceed@siam.org.
-%% A hardcopy version must also be submitted. Instructions are included
-%% in your acceptance letter. Please be sure to send hardcopy
-%% versions of any Postscript figures you have submitted electronically.
-%% Be sure to return your signed Copyright Transfer Agreement. We cannot
-%% publish your paper without it.
-%%
-%%
-%%
-%%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%-
-%%%
-
-
-\documentstyle[leqno,twoside,11pt,ltexnec]{article} %You must set up your
- %\documentstyle line like this.
-
-
-\begin{document}
-\cleardoublepage
-\pagestyle{myheadings}
-
-\title{Chapter 1\\
-NEC Proceedings Series Macros\\
- for Use With LaTeX\thanks{Any information regarding grants should be placed
-here.}}
-\author{J. Corey Gray\thanks{Production Manager, Society for Industrial and Applied
-Mathematics, Philadelphia, PA.}
-\and
-Tricia Manning\thanks{Publications Specialist, Society for Industrial and Applied
-Mathematics, Philadelphia, PA.}
-\and
-Vickie Kearn\thanks{Publisher, Society for Industrial and Applied Mathematics,
-Philadelphia, PA.}\\
-\and
-Nancy Abbott\thanks{Design Supervisor, Society for Industrial and Applied
-Mathematics, Philadelphia, PA}
-\and
-Sue Ciambrano\thanks{Acquisitions Editor, Society for Industrial and Applied
-Mathematics, Philadelphia, PA}
-\and
-Paul Duggan\thanks{Composition Specialist, Society for Industrial and Applied
-Mathematics, Philadelphia, PA}
-\and
-Robbi Anne Albert\thanks{Production Assistant, Society for Industrial and Applied
-Mathematics, Philadelphia, PA}
-\and
-Jean Anderson\thanks{Composition Coordinator, Society for Industrial and Applied
-Mathematics, Philadelphia, PA}
-}
-\date{}
-\maketitle
-\markboth{Gray et al.}{SIAM Proceedings Series Macros} % See section 5 above
- % for explanation.
-\pagenumbering{arabic}
-
-\begin{abstract}An equivalence is shown between realizability of input/output (i/o) operators by
-rational control systems and high-order algebraic differential equations for
-i/o pairs. This generalizes, to nonlinear systems, the equivalence
-between autoregressive representations and finite dimensional linear
-realizability. \end{abstract}
-\section{Problem Specification}In this paper, we consider the solution of the $N \times
-N$ linear
-system
-\begin{equation} \label{e1.1}
-\cos \sin A x = b
-\end{equation}
-where $A$ is large, sparse, symmetric, and positive definite. We consider
-the direct solution of (\ref{e1.1}) by means of general sparse Gaussian
-elimination. In such a procedure, we find a permutation matrix $P$, and
-compute the decomposition
-\[
-P A P^{t} = L D L^{t}
-\]
-where $L$ is unit lower triangular and $D$ is diagonal.
-
-
-\section{Design Considerations}Several good ordering algorithms (nested dissection and
-minimum degree)
-are available for computing $P$ \cite{GEORGELIU}, \cite{ROSE72}.
-Since our interest here does not
-focus directly on the ordering, we assume for convenience that $P=I$,
-or that $A$ has been preordered to reflect an appropriate choice of $P$.
-
-Our purpose here is to examine the nonnumerical complexity of the
-sparse elimination algorithm given in \cite{BANKSMITH}.
-As was shown there, a general sparse elimination scheme based on the
-bordering algorithm requires less storage for pointers and
-row/column indices than more traditional implementations of general
-sparse elimination. This is accomplished by exploiting the m-tree,
-a particular spanning tree for the graph of the filled-in matrix.
-
-\begin{theorem} The method was extended to three
-dimensions. For the standard multigrid
-coarsening
-(in which, for a given grid, the next coarser grid has $1/8$
-as many points), anisotropic problems require plane
-relaxation to
-obtain a good smoothing factor.\end{theorem}
-
-Several good ordering algorithms (nested dissection and minimum degree)
-are available for computing $P$ \cite{GEORGELIU}, \cite{ROSE72}.
-Since our interest here does not
-focus directly on the ordering, we assume for convenience that $P=I$,
-or that $A$ has been preordered to reflect an appropriate choice of $P$.
-
-
-\begin{proof} In this paper we consider two methods. The first method
-is
-basically the method considered with two differences:
-first, we perform plane relaxation by a two-dimensional
-multigrid method, and second, we use a slightly different
-choice of
-interpolation operator, which improves performance
-for nearly singular problems. In the second method coarsening
-is done by successively coarsening in each of the three
-independent variables and then ignoring the intermediate
-grids; this artifice simplifies coding considerably.\qed
-\end{proof}
-
-Our purpose here is to examine the nonnumerical complexity of the
-sparse elimination algorithm given in \cite{BANKSMITH}.
-As was shown there, a general sparse elimination scheme based on the
-bordering algorithm requires less storage for pointers and
-row/column indices than more traditional implementations of general
-sparse elimination. This is accomplished by exploiting the m-tree,
-a particular spanning tree for the graph of the filled-in matrix.
-
-\begin{Definition}{\rm We describe the two methods in \S 1.2. In \S\ 1.3. we
-discuss
-some remaining details.}
-\end{Definition}
-
-\begin{figure}
-\vspace*{24pc}
-\caption{This is figure 1.}
-\end{figure}
-
-Our purpose here is to examine the nonnumerical complexity of the
-sparse elimination algorithm given in \cite{BANKSMITH}.
-As was shown there, a general sparse elimination scheme based on the
-bordering algorithm requires less storage for pointers and
-row/column indices than more traditional implementations of general
-sparse elimination.
-
-\begin{lemma} We discuss first the choice for $I_{k-1}^k$
-which is a generalization. We assume that $G^{k-1}$ is
-obtained
-from $G^k$
-by standard coarsening; that is, if $G^k$ is a tensor product
-grid $G_{x}^k \times G_{y}^k \times G_{z}^k$,
-$G^{k-1}=G_{x}^{k-1} \times G_{y}^{k-1} \times G_{z}^{k-1}$,
-where $G_{x}^{k-1}$ is obtained by deleting every other grid
-point of $G_x^k$ and similarly for $G_{y}^k$ and $G_{z}^k$.
-\end{lemma}
-
-This is accomplished by exploiting the m-tree,
-a particular spanning tree for the graph of the filled-in matrix.
-To our knowledge, the m-tree previously has not been applied in this
-fashion to the numerical factorization, but it has been used,
-directly or indirectly, in several optimal order algorithms for
-computing the fill-in during the symbolic factorization phase
-\cite{EISENSTAT} - \cite{LIU2}, \cite{ROSE76}, \cite{SCHREIBER}.
-
-\subsection{Robustness}
-We do not
-attempt to present an overview
-here, but rather attempt to focus on those results that
-are relevant to our particular algorithm.
-This section assumes prior knowledge of the role of graph theory
-in sparse Gaussian elimination; surveys of this role are
-available in \cite{ROSE72} and \cite{GEORGELIU}. More general
-discussions of elimination trees are given in
-\cite{LAW} - \cite{LIU2}, \cite{SCHREIBER}.
-Thus, at the $k$th stage, the bordering algorithm consists of
-solving the lower triangular system
-\begin{equation} \label{1.2}
- L_{k-1}v = c
-\end{equation}
-and setting
-\begin{eqnarray}
-\ell &=& D^{-1}_{k-1}v , \\
-\delta &=& \alpha - \ell^{t} v .
-\end{eqnarray}
-
-\subsubsection{Versatility.} We do not
-attempt to present an overview
-here, but rather attempt to focus on those results that
-are relevant to our particular algorithm.
-
-\section{Conclusions} The special
-structure of this problem allows us to make exact estimates of
-the complexity. For the old approach, we show that the
-complexity of the intersection problem is $O(n^{3})$, the same
-as the complexity of the numerical computations
-\cite{GEORGELIU}, \cite{ROSEWHITTEN}. For the
-new approach, the complexity of the second part is reduced to
-$O(n^{2} (\log n)^{2})$.
-
-\begin{thebibliography}{99}
-
-
-\bibitem{BANKSMITH}
-R.~E. Bank and R.~K. Smith, {\em General sparse elimination requires no
- permanent integer storage}, SIAM J. Sci. Stat. Comput., 8 (1987),
- pp.~574--584.
-
-\bibitem{EISENSTAT}
-S.~C. Eisenstat, M.~C. Gursky, M.~Schultz, and A.~Sherman, {\em
- Algorithms and data structures for sparse symmetric gaussian elimination},
- SIAM J. Sci. Stat. Comput., 2 (1982), pp.~225--237.
-
-\bibitem{GEORGELIU}
-A.~George and J.~Liu, {\em Computer Solution of Large Sparse Positive
- Definite Systems}, Prentice Hall, Englewood Cliffs, NJ, 1981.
-
-\bibitem{LAW}
-K.~H. Law and S.~J. Fenves, {\em A node addition model for symbolic
- factorization}, ACM TOMS, 12 (1986), pp.~37--50.
-
-\bibitem{LIU}
-J.~W.~H. Liu, {\em A compact row storage scheme for cholesky factors
- using elimination trees}, ACM TOMS, 12 (1986), pp.~127--148.
-
-\bibitem{LIU2}
-\sameauthor , {\em The role of
- elimination trees in sparse factorization}, Tech. Report CS-87-12,Department
- of Computer Science, York University, Ontario, Canada, 1987.
-
-\bibitem{ROSE72}
-D.~J. Rose, {\em A graph theoretic study of the numeric solution of
- sparse positive definite systems}, in Graph Theory and Computing, AcademicΠPress, New
-York, 1972.
-
-\bibitem{ROSE76}
-D.~J. Rose, R.~E. Tarjan, and G.~S. Lueker, {\em Algorithmic aspects of
- vertex elimination on graphs}, SIAM J. Comput., 5 (1976), pp.~226--283.
-
-\bibitem{ROSEWHITTEN}
-D.~J. Rose and G.~F. Whitten, {\em A recursive analysis of disection
- strategies}, in Sparse Matrix Computations, Academic Press, New York, 1976.
-
-\bibitem{SCHREIBER}
-R.~Schrieber, {\em A new implementation of sparse gaussian elimination},
- ACM TOMS, 8 (1982), pp.~256--276.
-
-\end{thebibliography}
-
-\end{document}
-
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%CUT HERE%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-%
-%
-% This file may be freely distributed but may not be altered in any way.
-% Any comments or questions regarding these macros should be directed to:
-
-% Corey Gray
-% SIAM
-% 3600 University City Science Center
-% Philadelphia, PA 19104-2688
-% USA
-% Telephone: (215) 382-9800
-% Fax: (215) 386-7999
-% e-mail: gray@siam.org
-
-% This is a file of macros and definitions for creating a chapter for
-% publication in the NEC Proceedings series using LaTeX.
-
-% Report the version.
-\message{*** NEC LaTeX Proceedings Series macro package, version 1.0,
-July 10, 1992 ***}
-%\input proceed.sty
-
-\pretolerance=800
-\tolerance=10000
-\sloppy
-
-
-\vsize=49pc
-\hsize=30pc
-\baselineskip=13pt
-\hoffset -.5in
-\voffset -.5in
-\footskip=18pt
-\topmargin 24pt
-\headheight 12pt
-\headsep 17pt
-\textheight 49pc \advance\textheight by \topskip
-\textwidth 30pc
-\parskip 0pt
-\parindent 18pt
-\def\topfraction{.9}
-\def\textfraction{.1}
-\def\topnumber{2}
-%% footnotes to be set 8/10
-\def\footnotesize{\@setsize\footnotesize{11pt}\ixpt\@ixpt
- % \indent
- \abovedisplayskip \z@
- \belowdisplayskip\z@
- \abovedisplayshortskip\abovedisplayskip
- \belowdisplayshortskip\belowdisplayshortskip
-\def\@listi{\leftmargin\leftmargini \topsep 3pt plus 1pt minus 1pt
- \parsep 2pt plus 1pt minus 1pt
- \itemsep \parsep}}
-
-\let\referencesize\footnotesize
-
-\footnotesep 0pt
-
-\skip\footins 12pt plus 12pt
-
-\def\footnoterule{\kern3\p@ \hrule width 3em\vspace{3pt}} % the \hrule is
-%.4pt high
-
-
-\def\ps@plain{\let\@mkboth\@gobbletwo
- \def\@oddfoot{{\hfil\small\thepage\hfil}}%
- \def\@evenfoot{{\hfil\small\thepage\hfil}}%
-\def\@oddhead{}
- \def\@evenhead{}%\def\@evenfoot{}
-}
-
-
-
-\def\ps@headings{\let\@mkboth\markboth
- \def\@oddfoot{}\def\@evenfoot{}%
- \def\@evenhead{{\rm\thepage}\hspace*{2pc}{\small\leftmark}\hfil}%
-
-\def\@oddhead{\hfil{\noindent\small\rightmark}\hspace*{2pc}{\rm\thepage}}%
-
-% \def\chaptermark##1{\markboth{\uppercase{%
- % {\protect\small\@chapapp}\
-%{\protect\small\thechapter}}}%
- % {\uppercase{##1}}}%
- }
-
-
-\def\ps@myheadings{\let\@mkboth\@gobbletwo
- \def\@oddfoot{}\def\@evenfoot{}%
-
-\def\@oddhead{\hfil{\small\rightmark}\hspace*{2pc}{\normalsize\rm\thepage}}
-%
-
-\def\@evenhead{{\normalsize\rm\thepage}\hspace*{2pc}{\small\leftmark}\hfil}
-%
-% \def\chaptermark##1{}%
- % \def\sectionmark##1{}\def\subsectionmark##1{}}
-}
-
-
-
-\def\theequation{\arabic{equation}}
-%\def\theequation{\arabic{chapter}.\arabic{equation}}
-
-\def\abstract{\if@twocolumn
-\section*{Abstract}
-\else \small
-\begin{center}
-{\bf Abstract\vspace{-.5em}\vspace{3pt}}
-\end{center}
-\quotation
-\fi}
-\def\endabstract{\if@twocolumn\else\endquotation\fi}
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% %
-% THEOREMS, PROOFS, ALGORITHMS %
-% %
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-%%% defined proof environment by theorem model (took out counter)
-
-\def\newproof#1{\@nprf{#1}}
-
-\def\@nprf#1#2{\@xnprf{#1}{#2}}
-
-\def\@xnprf#1#2{\expandafter\@ifdefinable\csname #1\endcsname
-\global\@namedef{#1}{\@prf{#1}{#2}}\global\@namedef{end#1}{\@endproof}}
-
-\def\@prf#1#2{\@xprf{#1}{#2}}
-
-\def\@xprf#1#2{\@beginproof{#2}{\csname the#1\endcsname}\ignorespaces}
-
-
-
-%%% defined algorithm environment by theorem model
-
-\def\newalgorithm#1{\@ifnextchar[{\@oalg{#1}}{\@nalg{#1}}}
-
-\def\@nalg#1#2{%
-\@ifnextchar[{\@xnalg{#1}{#2}}{\@ynalg{#1}{#2}}}
-
-\def\@xnalg#1#2[#3]{\expandafter\@ifdefinable\csname #1\endcsname
-{\@definecounter{#1}\@addtoreset{#1}{#3}%
-\expandafter\xdef\csname the#1\endcsname{\expandafter\noexpand
- \csname the#3\endcsname \@thmcountersep \@thmcounter{#1}}%
-\global\@namedef{#1}{\@alg{#1}{#2}}\global\@namedef{end#1}{\@endalgorithm}}
-}
-
-\def\@ynalg#1#2{\expandafter\@ifdefinable\csname #1\endcsname
-{\@definecounter{#1}%
-\expandafter\xdef\csname the#1\endcsname{\@thmcounter{#1}}%
-\global\@namedef{#1}{\@alg{#1}{#2}}\global\@namedef{end#1}{\@endalgorithm}}
-}
-
-\def\@oalg#1[#2]#3{\expandafter\@ifdefinable\csname #1\endcsname
- {\global\@namedef{the#1}{\@nameuse{the#2}}%
-\global\@namedef{#1}{\@alg{#2}{#3}}%
-\global\@namedef{end#1}{\@endalgorithm}}}
-
-\def\@alg#1#2{\refstepcounter
- {#1}\@ifnextchar[{\@yalg{#1}{#2}}{\@xalg{#1}{#2}}}
-
-\def\@xalg#1#2{\@beginalgorithm{#2}{\csname the#1\endcsname}\ignorespaces}
-\def\@yalg#1#2[#3]{\@opargbeginalgorithm{#2}{\csname
- the#1\endcsname}{#3}\ignorespaces}
-
-
-
-
-\def\@beginproof#1{\rm {\it #1.\ }}
-\def\@endproof{\outerparskip 0pt\endtrivlist}
-
-\def\@begintheorem#1#2{\it {\sc #1\ #2.\ }}
-\def\@opargbegintheorem#1#2#3{\it
- {\sc #1\ #2\ (#3).\ }}
-\def\@endtheorem{\outerparskip 0pt\endtrivlist}
-
-%\def\@begindefinition#1#2{\rm \trivlist \item[\hskip \labelsep{\sc #1\#2.}]}
-%\def\@opargbegindefinition#1#2#3{\rm \trivlist
-% \item[\hskip \labelsep{\sc #1\ #2.\ (#3)}]}
-%\def\@enddefinition{\outerparskip 0pt\endtrivlist}
-
-
-\def\@beginalgorithm#1#2{\rm \trivlist \item[\hskip \labelsep{\sc #1\#2.}]}
-\def\@opargbeginalgorithm#1#2#3{\rm \trivlist
- \item[\hskip \labelsep{\sc #1\ #2.\ (#3)}]}
-\def\@endalgorithm{\outerparskip 6pt\endtrivlist}
-
-
-\newskip\outerparskip
-
-\def\trivlist{\parsep\outerparskip
- \@trivlist \labelwidth\z@ \leftmargin\z@
- \itemindent\parindent \def\makelabel##1{##1}}
-
-\def\@trivlist{\topsep=0pt\@topsepadd\topsep
- \if@noskipsec \leavevmode \fi
- \ifvmode \advance\@topsepadd\partopsep \else \unskip\par\fi
- \if@inlabel \@noparitemtrue \@noparlisttrue
- \else \@noparlistfalse \@topsep\@topsepadd \fi
- \advance\@topsep \parskip
- \leftskip\z@\rightskip\@rightskip \parfillskip\@flushglue
- \@setpar{\if@newlist\else{\@@par}\fi}%
- \global\@newlisttrue \@outerparskip\parskip}
-
-
-\def\endtrivlist{\if@newlist\@noitemerr\fi
- \if@inlabel\indent\fi
- \ifhmode\unskip \par\fi
- \if@noparlist \else
- \ifdim\lastskip >\z@ \@tempskipa\lastskip \vskip -\lastskip
- \advance\@tempskipa\parskip \advance\@tempskipa -\@outerparskip
- \vskip\@tempskipa
- \fi\@endparenv\fi
- \vskip\outerparskip}
-
-
-
- \newproof{@proof}{Proof}
- \newenvironment{proof}{\begin{@proof}}{\end{@proof}}
-
- \newtheorem{@theorem}{Theorem}[section]
- \newenvironment{theorem}{\begin{@theorem}}{\end{@theorem}}
-
-% \newalgorithm{@algorithm}{Algorithm}[section]
-% \newenvironment{algorithm}{\begin{@algorithm}}{\end{@algorithm}}
-
-
-
-\newtheorem{lemma}{Lemma}[section]
-\newtheorem{fact}{Fact}[section]
-\newtheorem{corollary}{Corollary}[section]
-\newtheorem{axiom}{Axiom}[section]
-\newtheorem{cond}{Condition}[section]
-\newtheorem{property}{Property}[section]
-\newtheorem{proposition}{Proposition}[section]
-
-\newtheorem{Conjecture}{Conjecture}[section]
-\newtheorem{Corollary}{Corollary}[section]
-\newtheorem{Definition}{Definition}[section]
-\newtheorem{Lemma}{Lemma}[section]
-\newtheorem{Remark}{Remark}[section]
-
-\newproof{Example}{Example}
-\newproof{Method}{Method}
-\newproof{Exercise}{Exercise}
-
-\def\qed{{\qquad \vbox{\hrule\hbox{%
- \vrule height1.3ex\hskip0.8ex\vrule}\hrule
- }}\par}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% %
-% TABLE AND FIGURE CAPTIONS %
-% %
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \def\@figtxt{figure}
-\long\def\@makecaption#1#2{\small
-\setlength{\parindent}{18pt}
-\baselineskip 14pt
- \ifx\@captype\@figtxt
- \vskip 10pt
- \setbox\@tempboxa\hbox{{\sc #1} {\it #2}}
- \ifdim \wd\@tempboxa >\hsize {\sc #1} {\it #2}\par \else \hbox
-to\hsize{\hfil\box\@tempboxa\hfil}%
- \fi\else\hbox to\hsize{\hfil{\sc #1}\hfil}%
- \setbox\@tempboxa\hbox{{\it #2}}%
- \ifdim \wd\@tempboxa >\hsize {\it #2}\par \else
- \hbox to \hsize{\hfil\box\@tempboxa\hfil}\fi
- \vskip 10pt
- \fi}
-
-
-%\newif\iftable \global\tablefalse
-
-
-%\long\def\@makecaption#1#2{%
-%\setlength{\parindent}{18pt}
-% \vskip 12pt
-% \iftable
- % \hbox to \hsize{\hfil\sc #1\hfil}
- % \hbox to \hsize{\hfil\it #2\hfil}
- % \global\tablefalse
- % \else
- % \setbox\@tempboxa\hbox{{\small#1} {\small\it#2}}
- % \ifdim \wd\@tempboxa >\hsize
- % \indent{\small#1}{\small\it#2}\par
- % \else
- % \hbox to\hsize{\hfil\box\@tempboxa\hfil}\fi
- % \fi}
-% \vskip 6pt}
-
-
-
-%\def\figure{\global\tablefalse\@float{figure}}
-\def\fnum@figure{\par\sc Fig. \thefigure.\ }
-%\def\fnum@figure{\par\sc Fig. \thefigure\ }
-
-%\def\table{\global\tabletrue\@float{table}}
-\def\fnum@table{\small \sc Table \thetable}
-
-
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% %
-% CHAPTER %
-% %
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-%\def\@chapapp{Chapter}
-
-%\def\@makechapterhead#1{%
- % \vspace*{8pt}
- % \vtop to 11pc{\leftskip=0pc \parindent 0pt
- % \begin{center}{\large \@chapapp}%\end{flushright}%%%
- % {\large \baselineskip=26pt\ \thechapter}\end{center}\vskip-8pt
-% \vrule width 31pc height .5pt\par %
- % \vspace*{6pt}%
- % \baselineskip=18pt\begin{center}{\Large#1 }\end{center}\par
- % \vfil}}
-
-%\def\@makeschapterhead#1{%
- % \vspace*{8pt}
- % \vtop to 11pc{\leftskip=0pc \parindent 0pt
- % \vtop to 26pt{\vfill}\vskip-8pt
- % \vrule width 31pc height .5pt\par %
-% % \vspace*{6pt}%
- % {\Large #1}\par
- % \vfil}}
-
-
-%\def\chapter{\cleardoublepage \thispagestyle{plain} \global\@topnum\z@
- % \@afterindentfalse \secdef\@chapter\@schapter}
-
-%\def\author#1{\vspace*{-6.25pc}\begin{center}{#1}\end{center}
- % \par\vspace*{4pc}}
-%\def\chaptermark#1{}
-
-%\def\@chapter[#1]#2{%
- % \refstepcounter{chapter}
- % \typeout{Chapter\space\thechapter.}
-% % \addcontentsline{toc}{chapter}{CHAPTER\ \thechapter. #1}
- % \protect\addtocontents{lof}{\protect\addvspace{10pt}}
- % \protect\addtocontents{lot}{\protect\addvspace{10pt}}
- % \chaptermark{#1}
- % \@makechapterhead{#2}
- % \@afterheading}
-
-
-
-%\def\@schapter#1{\@makeschapterhead{#1}
- % \@afterheading}
-
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% %
-% SECTIONS %
-% %
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-\def\section{\@startsection {section}{1}{\z@}{-3.5ex plus -1ex minus
- -.2ex}{2.3ex plus .2ex}{\large\bf}}
-\def\subsection{\@startsection{subsection}{2}{\z@}{-3.25ex plus -1ex minus
- -.2ex}{1.5ex plus .2ex}{\large\bf}}
-\def\subsubsection{\@startsection{subsubsection}{3}{\z@}{-3.25ex plus
- -1ex minus -.2ex}{1.5ex plus .2ex}{\large\bf}}
-%\renewcommand{\section}{\@startsection {section}{1}{\z@}{-3.5ex plus -1ex
-%minus
-% -.2ex}{2.3ex plus .2ex}{\large\bf}}
-
-%\def\@sect#1#2#3#4#5#6[#7]#8{\ifnum #2>\c@secnumdepth
-% \def\@svsec{}\else
-% \refstepcounter{#1}\edef\@svsec{\csname the#1\endcsname.\hskip .75em
-%}\fi%
-%
- % \@tempskipa #5\relax
- % \ifdim \@tempskipa>\z@
- % \begingroup #6\relax
- % \@hangfrom{\hskip #3\relax\@svsec}{\interlinepenalty \@M #8\par}
- % \endgroup
-% \csname #1mark\endcsname{#7}\addcontentsline
- %{toc}{#1}{\ifnum #2>\c@secnumdepth \else
- % \protect\numberline{\csname the#1\endcsname}\fi
- % #7}\else
- % \def\@svsechd{#6\hskip #3\@svsec #8\hskip1em\csname #1mark\endcsname
-
- % {#7}\addcontentsline
- % {toc}{#1}{\ifnum #2>\c@secnumdepth \else
- % \protect\numberline{\csname the#1\endcsname}\fi
- % #7}}\fi
- % \@xsect{#5}}
-
-
- %\@startsection {NAME}{LEVEL}{INDENT}{BEFORESKIP}{AFTERSKIP}{STYLE}
-%\def\section{\@startsection{section}{1}{0pt}{-12pt}{3pt}{\hyphenpenalty=\@
-%M
-%\exhyphenpenalty=\@M\normalsize\bf}}
-%\def\subsection{\@startsection{subsection}{2}{0pt}{-12pt}{0pt}{\normalsize
-%\bf}
-%}
-%\def\subsubsection{\@startsection
-% {subsubsection}{3}{0pt}{-12pt}{0pt}{\normalsize\bf}}
-%\def\paragraph{\@startsection
-% {paragraph}{4}{\parindent}{0pt}{0pt}{\normalsize\bf}}
-%\def\subparagraph{\@startsection
-% {subparagraph}{4}{\parindent}{0pt}{0pt}{\normalsize\bf}}
-%\def\thepart{\Roman{part}}
-%\def\thesection {\arabic{section}.}
-%\def\thesubsection {\thesection\arabic{subsection}.}
-%\def\thesubsubsection {\thesubsection .\arabic{subsubsection}.}
-%\def\theparagraph {\thesubsubsection.\arabic{paragraph}.}
-%\def\thesubparagraph {\theparagraph.\arabic{subparagraph}.}
-
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% %
-% TOC %
-% %
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-%% sets chapter in toc
-%\def\l@chapter#1#2{\pagebreak[3]
-% \hbox to \hsize{\null\hskip2pc
-% \llap{\hbox to\@pnumwidth{\hss#2}\hskip2pc}%
-% #1\hfill}\vskip1pc}
-
-
-%%% set so only chapters print in TOC
-%\def\@dottedtocline#1#2#3#4#5{\relax}
-
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% %%
-%% BIBLIOGRAPHY %%
-%% %%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-
-\def\thebibliography#1{%
-%\cleardoublepage
-\parindent 0em
-\vspace{9pt}
-\begin{flushleft}\large\bf {References}\end{flushleft}
-\addvspace{3pt}\nopagebreak\list
- %% default is no labels, for those not using \cite or BibTeX
-{[\arabic{enumi}]} {\settowidth\labelwidth{[#1]}
-%%{[\arabic{enumi}]}{\settowidth\labelwidth{mm}
-\leftmargin\labelwidth
-\leftmargin=12pt
- \advance\leftmargin\labelsep
- \usecounter{enumi}\@bibsetup}
-\def\newblock{\hskip .11em plus .33em minus -.07em}
- \sloppy\clubpenalty4000\widowpenalty4000
- \sfcode`\.=1000\relax}
-
-%\def\thebibliography#1{%
-%\cleardoublepage
-%\parindent 0em
-%\vspace{9pt}
-%\begin{flushleft}\Large\bf{References} \end{flushleft}
-%\addvspace{3pt}\nopagebreak\list
-%% %% default is no labels, for those not using \cite or BibTeX
-%%% {[\arabic{enumi}]} {\settowidth\labelwidth{[#1]}
-%{[\arabic{enumi}]}{\settowidth\labelwidth{mm}
-%%{}{\settowidth\labelwidth{mm}
-%\leftmargin\labelwidth
-%\advance
-%\leftmargin 0pt \itemindent -16pt
-% \usecounter{enumi}\@bibsetup}
-%\def\newblock{\hskip .11em plus .33em minus -.07em}
-% \sloppy\clubpenalty4000\widowpenalty4000
-% \sfcode`\.=1000\relax}
-
-%% setup 8/10 type
-\def\@bibsetup{%\itemindent=0pt
-\itemsep=0pt \parsep=0pt
-\small}
-
-\def\sameauthor{\leavevmode\vrule height 2pt depth -1.6pt width 23pt}
-
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% %
-% INDEX %
-% %
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-
-%makeindex.sty official version 6.4
-%The second line came from /usr/misc/lib/tex82/report.sty.
-
-\def\theindex{\@restonecoltrue\if@twocolumn\@restonecolfalse\fi
-\columnseprule \z@
-\columnsep 35pt\twocolumn[\chapter*{Index}]
- \parskip\z@ plus .3pt\relax\let\item\@idxitem}
-
-
-\def\printindex{\cleardoublepage\markboth{INDEX}{INDEX}
-\addcontentsline{toc}{chapter}{Index}\@input{\jobname.ind}}
-
-\ps@headings
-
-
-%%% end of original style file
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%CUT HERE%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-
-% SIAM bibliography style (29-Jan-88 version)
-% numeric labels, alphabetic order, Mathematical Reviews abbreviations,
-% names in \sc, titles in italics, book titles mixed upper-lower and article
-% titles lowercase, commas separate all fields except before "notes".
-%
-% History
-% 1/30/86 (HWT) Original version, by Howard Trickey.
-% 6/15/87 (HWT) Fix format.editors---Martin Costabel.
-% 1/29/88 (OP&HWT) Updated for BibTeX version 0.99a, Oren Patashnik;
-% THIS `siam' VERSION DOES NOT WORK WITH BIBTEX 0.98i.
-
-ENTRY
- { address
- author
- booktitle
- chapter
- edition
- editor
- howpublished
- institution
- journal
- key
- month
- note
- number
- organization
- pages
- publisher
- school
- series
- title
- type
- volume
- year
- }
- {}
- { label }
-
-INTEGERS { output.state before.all mid.sentence after.block }
-
-FUNCTION {init.state.consts}
-{ #0 'before.all :=
- #1 'mid.sentence :=
- #2 'after.block :=
-}
-
-STRINGS { s t }
-
-FUNCTION {output.nonnull}
-{ 's :=
- output.state mid.sentence =
- { ", " * write$ }
- { output.state after.block =
- { add.period$ write$
- newline$
- "\newblock " write$
- }
- 'write$
- if$
- mid.sentence 'output.state :=
- }
- if$
- s
-}
-
-FUNCTION {output}
-{ duplicate$ empty$
- 'pop$
- 'output.nonnull
- if$
-}
-
-FUNCTION {output.check}
-{ 't :=
- duplicate$ empty$
- { pop$ "empty " t * " in " * cite$ * warning$ }
- 'output.nonnull
- if$
-}
-
-FUNCTION {output.bibitem}
-{ newline$
- "\bibitem{" write$
- cite$ write$
- "}" write$
- newline$
- ""
- before.all 'output.state :=
-}
-
-FUNCTION {fin.entry}
-{ add.period$
- write$
- newline$
-}
-
-FUNCTION {new.block}
-{ output.state before.all =
- 'skip$
- { after.block 'output.state := }
- if$
-}
-
-FUNCTION {not}
-{ { #0 }
- { #1 }
- if$
-}
-
-FUNCTION {and}
-{ 'skip$
- { pop$ #0 }
- if$
-}
-
-FUNCTION {or}
-{ { pop$ #1 }
- 'skip$
- if$
-}
-
-FUNCTION {new.block.checka}
-{ empty$
- 'skip$
- 'new.block
- if$
-}
-
-FUNCTION {field.or.null}
-{ duplicate$ empty$
- { pop$ "" }
- 'skip$
- if$
-}
-
-FUNCTION {emphasize}
-{ duplicate$ empty$
- { pop$ "" }
- { "{\em " swap$ * "}" * }
- if$
-}
-
-FUNCTION {scapify}
-{ duplicate$ empty$
- { pop$ "" }
- { "{\sc " swap$ * "}" * }
- if$
-}
-
-INTEGERS { nameptr namesleft numnames }
-
-FUNCTION {format.names}
-{ 's :=
- #1 'nameptr :=
- s num.names$ 'numnames :=
- numnames 'namesleft :=
- { namesleft #0 > }
- { s nameptr "{f.~}{vv~}{ll}{, jj}" format.name$ 't :=
- nameptr #1 >
- { namesleft #1 >
- { ", " * t * }
- { numnames #2 >
- { "," * }
- 'skip$
- if$
- t "others" =
- { " et~al." * }
- { " and " * t * }
- if$
- }
- if$
- }
- 't
- if$
- nameptr #1 + 'nameptr :=
- namesleft #1 - 'namesleft :=
- }
- while$
-}
-
-STRINGS { last.authors }
-
-FUNCTION {init.last.authors}
-{ "" 'last.authors :=
-}
-
-FUNCTION {format.authors}
-{ author empty$
- { "" 'last.authors :=
- ""
- }
- { author last.authors =
- { "\leavevmode\vrule height 2pt depth -1.6pt width 23pt" }
- { author format.names }% scapify }
- if$
- author 'last.authors :=
- }
- if$
-}
-
-FUNCTION {format.organization}
-{ organization empty$
- { "" 'last.authors :=
- ""
- }
- { organization last.authors =
- { "\leavevmode\vrule height 2pt depth -1.6pt width 23pt" }
- { organization scapify }
- if$
- organization 'last.authors :=
- }
- if$
-}
-
-FUNCTION {format.editors}
-{ editor empty$
- { "" 'last.authors :=
- ""
- }
- { editor last.authors =
- { "\leavevmode\vrule height 2pt depth -1.6pt width 23pt" }
- { editor format.names scapify }
- if$
- editor num.names$ #1 >
- { ", eds." * }
- { ", ed." * }
- if$
- editor 'last.authors :=
- }
- if$
-}
-
-FUNCTION {format.ineditors}
-{ editor empty$
- { "" }
- { editor format.names
- editor num.names$ #1 >
- { ", eds." * }
- { ", ed." * }
- if$
- }
- if$
-}
-
-FUNCTION {format.title}
-{ title empty$
- { "" }
- { title "t" change.case$ emphasize }
- if$
-}
-
-FUNCTION {n.dashify}
-{ 't :=
- ""
- { t empty$ not }
- { t #1 #1 substring$ "-" =
- { t #1 #2 substring$ "--" = not
- { "--" *
- t #2 global.max$ substring$ 't :=
- }
- { { t #1 #1 substring$ "-" = }
- { "-" *
- t #2 global.max$ substring$ 't :=
- }
- while$
- }
- if$
- }
- { t #1 #1 substring$ *
- t #2 global.max$ substring$ 't :=
- }
- if$
- }
- while$
-}
-
-FUNCTION {format.date}
-{ year empty$
- { month empty$
- { "" }
- { "there's a month but no year in " cite$ * warning$
- month
- }
- if$
- }
- { month empty$
- 'year
- { month " " * year * }
- if$
- }
- if$
-}
-
-FUNCTION {format.btitle}
-{ title emphasize
-}
-
-FUNCTION {tie.or.space.connect}
-{ duplicate$ text.length$ #3 <
- { "~" }
- { " " }
- if$
- swap$ * *
-}
-
-FUNCTION {either.or.check}
-{ empty$
- 'pop$
- { "can't use both " swap$ * " fields in " * cite$ * warning$ }
- if$
-}
-
-FUNCTION {format.bvolume}
-{ volume empty$
- { "" }
- { "vol.~" volume *
- series empty$
- 'skip$
- { " of " * series * }
- if$
- "volume and number" number either.or.check
- }
- if$
-}
-
-FUNCTION {format.number.series}
-{ volume empty$
- { number empty$
- { series field.or.null }
- { "no.~" number *
- series empty$
- { "there's a number but no series in " cite$ * warning$ }
- { " in " * series * }
- if$
- }
- if$
- }
- { "" }
- if$
-}
-
-FUNCTION {format.edition}
-{ edition empty$
- { "" }
- { edition "l" change.case$ "~ed." * }
- if$
-}
-
-INTEGERS { multiresult }
-
-FUNCTION {multi.page.check}
-{ 't :=
- #0 'multiresult :=
- { multiresult not
- t empty$ not
- and
- }
- { t #1 #1 substring$
- duplicate$ "-" =
- swap$ duplicate$ "," =
- swap$ "+" =
- or or
- { #1 'multiresult := }
- { t #2 global.max$ substring$ 't := }
- if$
- }
- while$
- multiresult
-}
-
-FUNCTION {format.pages}
-{ pages empty$
- { "" }
- { pages multi.page.check
- { "pp.~" pages n.dashify * }
- { "p.~" pages * }
- if$
- }
- if$
-}
-
-FUNCTION {format.vol.year}
-{ volume field.or.null
- year empty$
- { "empty year in " cite$ * warning$ }
- { " (" year * ")" * * }
- if$
-}
-
-FUNCTION {format.chapter.pages}
-{ chapter empty$
- 'format.pages
- { type empty$
- { "ch.~" chapter * }
- { type "l" change.case$ chapter tie.or.space.connect }
- if$
- pages empty$
- 'skip$
- { ", " * format.pages * }
- if$
- }
- if$
-}
-
-FUNCTION {format.in.ed.booktitle}
-{ booktitle empty$
- { "" }
- { editor empty$
- { "in " booktitle * }
- { "in " booktitle * ", " * format.ineditors * }
- if$
- }
- if$
-}
-
-FUNCTION {empty.misc.check}
-{ author empty$ title empty$ howpublished empty$
- month empty$ year empty$ note empty$
- and and and and and
- key empty$ not and
- { "all relevant fields are empty in " cite$ * warning$ }
- 'skip$
- if$
-}
-
-FUNCTION {format.thesis.type}
-{ type empty$
- 'skip$
- { pop$
- type "l" change.case$
- }
- if$
-}
-
-FUNCTION {format.tr.number}
-{ type empty$
- { "Tech. Rep." }
- 'type
- if$
- number empty$
- { "l" change.case$ }
- { number tie.or.space.connect }
- if$
-}
-
-FUNCTION {format.article.crossref}
-{ key empty$
- { journal empty$
- { "need key or journal for " cite$ * " to crossref " * crossref *
- warning$
- ""
- }
- { "in " journal * }
- if$
- }
- { "in " key * }
- if$
- " \cite{" * crossref * "}" *
-}
-
-FUNCTION {format.crossref.editor}
-{ editor #1 "{vv~}{ll}" format.name$
- editor num.names$ duplicate$
- #2 >
- { pop$ " et~al." * }
- { #2 <
- 'skip$
- { editor #2 "{ff }{vv }{ll}{ jj}" format.name$ "others" =
- { " et~al." * }
- { " and " * editor #2 "{vv~}{ll}" format.name$ * }
- if$
- }
- if$
- }
- if$
-}
-
-FUNCTION {format.book.crossref}
-{ volume empty$
- { "empty volume in " cite$ * "'s crossref of " * crossref * warning$
- "in "
- }
- { "vol.~" volume *
- " of " *
- }
- if$
- editor empty$
- editor field.or.null author field.or.null =
- or
- { key empty$
- { series empty$
- { "need editor, key, or series for " cite$ * " to crossref " *
- crossref * warning$
- "" *
- }
- { series * }
- if$
- }
- { key * }
- if$
- }
- { format.crossref.editor * }
- if$
- " \cite{" * crossref * "}" *
-}
-
-FUNCTION {format.incoll.inproc.crossref}
-{ editor empty$
- editor field.or.null author field.or.null =
- or
- { key empty$
- { booktitle empty$
- { "need editor, key, or booktitle for " cite$ * " to crossref " *
- crossref * warning$
- ""
- }
- { "in " booktitle * }
- if$
- }
- { "in " key * }
- if$
- }
- { "in " format.crossref.editor * }
- if$
- " \cite{" * crossref * "}" *
-}
-
-FUNCTION {article}
-{ output.bibitem
- format.authors "author" output.check
- format.title "title" output.check
- crossref missing$
- { journal "journal" output.check
- format.vol.year output
- }
- { format.article.crossref output.nonnull }
- if$
- format.pages output
- new.block
- note output
- fin.entry
-}
-
-FUNCTION {book}
-{ output.bibitem
- author empty$
- { format.editors "author and editor" output.check }
- { format.authors output.nonnull
- crossref missing$
- { "author and editor" editor either.or.check }
- 'skip$
- if$
- }
- if$
- format.btitle "title" output.check
- crossref missing$
- { format.bvolume output
- format.number.series output
- publisher "publisher" output.check
- address output
- }
- { format.book.crossref output.nonnull }
- if$
- format.edition output
- format.date "year" output.check
- new.block
- note output
- fin.entry
-}
-
-FUNCTION {booklet}
-{ output.bibitem
- format.authors output
- format.title "title" output.check
- howpublished new.block.checka
- howpublished output
- address output
- format.date output
- new.block
- note output
- fin.entry
-}
-
-FUNCTION {inbook}
-{ output.bibitem
- author empty$
- { format.editors "author and editor" output.check }
- { format.authors output.nonnull
- crossref missing$
- { "author and editor" editor either.or.check }
- 'skip$
- if$
- }
- if$
- format.btitle "title" output.check
- crossref missing$
- { format.bvolume output
- format.number.series output
- publisher "publisher" output.check
- address output
- }
- { format.book.crossref output.nonnull }
- if$
- format.edition output
- format.date "year" output.check
- format.chapter.pages "chapter and pages" output.check
- new.block
- note output
- fin.entry
-}
-
-FUNCTION {incollection}
-{ output.bibitem
- format.authors "author" output.check
- format.title "title" output.check
- crossref missing$
- { format.in.ed.booktitle "booktitle" output.check
- format.bvolume output
- format.number.series output
- publisher "publisher" output.check
- address output
- format.edition output
- format.date "year" output.check
- }
- { format.incoll.inproc.crossref output.nonnull }
- if$
- format.chapter.pages output
- new.block
- note output
- fin.entry
-}
-
-FUNCTION {inproceedings}
-{ output.bibitem
- format.authors "author" output.check
- format.title "title" output.check
- crossref missing$
- { format.in.ed.booktitle "booktitle" output.check
- format.bvolume output
- format.number.series output
- address empty$
- { organization output
- publisher output
- format.date "year" output.check
- }
- { address output.nonnull
- format.date "year" output.check
- organization output
- publisher output
- }
- if$
- }
- { format.incoll.inproc.crossref output.nonnull }
- if$
- format.pages output
- new.block
- note output
- fin.entry
-}
-
-FUNCTION {conference} { inproceedings }
-
-FUNCTION {manual}
-{ output.bibitem
- author empty$
- { format.organization output }
- { format.authors output.nonnull }
- if$
- format.btitle "title" output.check
- author empty$
- 'skip$
- { organization output }
- if$
- address output
- format.edition output
- format.date output
- new.block
- note output
- fin.entry
-}
-
-FUNCTION {mastersthesis}
-{ output.bibitem
- format.authors "author" output.check
- format.title "title" output.check
- "Master's thesis" format.thesis.type output.nonnull
- school "school" output.check
- address output
- format.date "year" output.check
- new.block
- note output
- fin.entry
-}
-
-FUNCTION {misc}
-{ output.bibitem
- format.authors output
- format.title output
- howpublished new.block.checka
- howpublished output
- format.date output
- new.block
- note output
- fin.entry
- empty.misc.check
-}
-
-FUNCTION {phdthesis}
-{ output.bibitem
- format.authors "author" output.check
- format.btitle "title" output.check
- "PhD thesis" format.thesis.type output.nonnull
- school "school" output.check
- address output
- format.date "year" output.check
- new.block
- note output
- fin.entry
-}
-
-FUNCTION {proceedings}
-{ output.bibitem
- editor empty$
- { format.organization output }
- { format.editors output.nonnull }
- if$
- format.btitle "title" output.check
- format.bvolume output
- format.number.series output
- address empty$
- { editor empty$
- 'skip$
- { organization output }
- if$
- publisher output
- format.date "year" output.check
- }
- { address output.nonnull
- format.date "year" output.check
- editor empty$
- 'skip$
- { organization output }
- if$
- publisher output
- }
- if$
- new.block
- note output
- fin.entry
-}
-
-FUNCTION {techreport}
-{ output.bibitem
- format.authors "author" output.check
- format.title "title" output.check
- format.tr.number output.nonnull
- institution "institution" output.check
- address output
- format.date "year" output.check
- new.block
- note output
- fin.entry
-}
-
-FUNCTION {unpublished}
-{ output.bibitem
- format.authors "author" output.check
- format.title "title" output.check
- new.block
- note "note" output.check
- format.date output
- fin.entry
-}
-
-FUNCTION {default.type} { misc }
-
-MACRO {jan} {"Jan."}
-
-MACRO {feb} {"Feb."}
-
-MACRO {mar} {"Mar."}
-
-MACRO {apr} {"Apr."}
-
-MACRO {may} {"May"}
-
-MACRO {jun} {"June"}
-
-MACRO {jul} {"July"}
-
-MACRO {aug} {"Aug."}
-
-MACRO {sep} {"Sept."}
-
-MACRO {oct} {"Oct."}
-
-MACRO {nov} {"Nov."}
-
-MACRO {dec} {"Dec."}
-
-MACRO {acmcs} {"ACM Comput. Surveys"}
-
-MACRO {acta} {"Acta Inf."}
-
-MACRO {cacm} {"Comm. ACM"}
-
-MACRO {ibmjrd} {"IBM J. Res. Dev."}
-
-MACRO {ibmsj} {"IBM Syst.~J."}
-
-MACRO {ieeese} {"IEEE Trans. Softw. Eng."}
-
-MACRO {ieeetc} {"IEEE Trans. Comput."}
-
-MACRO {ieeetcad}
- {"IEEE Trans. Comput.-Aided Design Integrated Circuits"}
-
-MACRO {ipl} {"Inf. Process. Lett."}
-
-MACRO {jacm} {"J.~Assoc. Comput. Mach."}
-
-MACRO {jcss} {"J.~Comput. System Sci."}
-
-MACRO {scp} {"Sci. Comput. Programming"}
-
-MACRO {sicomp} {"SIAM J. Comput."}
-
-MACRO {tocs} {"ACM Trans. Comput. Syst."}
-
-MACRO {tods} {"ACM Trans. Database Syst."}
-
-MACRO {tog} {"ACM Trans. Gr."}
-
-MACRO {toms} {"ACM Trans. Math. Softw."}
-
-MACRO {toois} {"ACM Trans. Office Inf. Syst."}
-
-MACRO {toplas} {"ACM Trans. Prog. Lang. Syst."}
-
-MACRO {tcs} {"Theoretical Comput. Sci."}
-
-READ
-
-FUNCTION {sortify}
-{ purify$
- "l" change.case$
-}
-
-INTEGERS { len }
-
-FUNCTION {chop.word}
-{ 's :=
- 'len :=
- s #1 len substring$ =
- { s len #1 + global.max$ substring$ }
- 's
- if$
-}
-
-FUNCTION {sort.format.names}
-{ 's :=
- #1 'nameptr :=
- ""
- s num.names$ 'numnames :=
- numnames 'namesleft :=
- { namesleft #0 > }
- { nameptr #1 >
- { " " * }
- 'skip$
- if$
- s nameptr "{vv{ } }{ll{ }}{ f{ }}{ jj{ }}" format.name$ 't :=
- nameptr numnames = t "others" = and
- { "et al" * }
- { t sortify * }
- if$
- nameptr #1 + 'nameptr :=
- namesleft #1 - 'namesleft :=
- }
- while$
-}
-
-FUNCTION {sort.format.title}
-{ 't :=
- "A " #2
- "An " #3
- "The " #4 t chop.word
- chop.word
- chop.word
- sortify
- #1 global.max$ substring$
-}
-
-FUNCTION {author.sort}
-{ author empty$
- { key empty$
- { "to sort, need author or key in " cite$ * warning$
- ""
- }
- { key sortify }
- if$
- }
- { author sort.format.names }
- if$
-}
-
-FUNCTION {author.editor.sort}
-{ author empty$
- { editor empty$
- { key empty$
- { "to sort, need author, editor, or key in " cite$ * warning$
- ""
- }
- { key sortify }
- if$
- }
- { editor sort.format.names }
- if$
- }
- { author sort.format.names }
- if$
-}
-
-FUNCTION {author.organization.sort}
-{ author empty$
- { organization empty$
- { key empty$
- { "to sort, need author, organization, or key in " cite$ * warning$
- ""
- }
- { key sortify }
- if$
- }
- { "The " #4 organization chop.word sortify }
- if$
- }
- { author sort.format.names }
- if$
-}
-
-FUNCTION {editor.organization.sort}
-{ editor empty$
- { organization empty$
- { key empty$
- { "to sort, need editor, organization, or key in " cite$ * warning$
- ""
- }
- { key sortify }
- if$
- }
- { "The " #4 organization chop.word sortify }
- if$
- }
- { editor sort.format.names }
- if$
-}
-
-FUNCTION {presort}
-{ type$ "book" =
- type$ "inbook" =
- or
- 'author.editor.sort
- { type$ "proceedings" =
- 'editor.organization.sort
- { type$ "manual" =
- 'author.organization.sort
- 'author.sort
- if$
- }
- if$
- }
- if$
- " "
- *
- year field.or.null sortify
- *
- " "
- *
- title field.or.null
- sort.format.title
- *
- #1 entry.max$ substring$
- 'sort.key$ :=
-}
-
-ITERATE {presort}
-
-SORT
-
-STRINGS { longest.label }
-
-INTEGERS { number.label longest.label.width }
-
-FUNCTION {initialize.longest.label}
-{ "" 'longest.label :=
- #1 'number.label :=
- #0 'longest.label.width :=
-}
-
-FUNCTION {longest.label.pass}
-{ number.label int.to.str$ 'label :=
- number.label #1 + 'number.label :=
- label width$ longest.label.width >
- { label 'longest.label :=
- label width$ 'longest.label.width :=
- }
- 'skip$
- if$
-}
-
-EXECUTE {initialize.longest.label}
-
-ITERATE {longest.label.pass}
-
-FUNCTION {begin.bib}
-{ preamble$ empty$
- 'skip$
- { preamble$ write$ newline$ }
- if$
- "\begin{thebibliography}{" longest.label * "}" * write$ newline$
-}
-
-EXECUTE {begin.bib}
-
-EXECUTE {init.state.consts}
-
-EXECUTE {init.last.authors}
-
-ITERATE {call.type$}
-
-FUNCTION {end.bib}
-{ newline$
- "\end{thebibliography}" write$ newline$
-}
-
-EXECUTE {end.bib} \ No newline at end of file
diff --git a/Master/texmf-dist/source/latex/siam/ltexpprt.all b/Master/texmf-dist/source/latex/siam/ltexpprt.all
deleted file mode 100644
index 907e77cfeec..00000000000
--- a/Master/texmf-dist/source/latex/siam/ltexpprt.all
+++ /dev/null
@@ -1,702 +0,0 @@
-%% This is ltexpprt.all. This file is to be used for creating a paper
-%% in the ACM/SIAM Preprint series with LaTeX. It consists of the following
-%% two files:
-%%
-%% ltexpprt.tex ---- an example and documentation file
-%% ltexpprt.sty ---- the macro file
-%%
-%% To use, cut this file apart at the appropriate places. You can run the
-%% example file with the macros to get sample output.
-%%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%% CUT HERE %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%
-%
-%%%%%%%%%%%%%%%%%%%%%%%%%% ltexpprt.tex %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%
-% This is ltexpprt.tex, an example file for use with the SIAM LaTeX
-% Preprint Series macros. It is designed to provide double-column output.
-% Please take the time to read the following comments, as they document
-% how to use these macros. This file can be composed and printed out for
-% use as sample output.
-
-% Any comments or questions regarding these macros should be directed to:
-%
-% Corey Gray
-% SIAM
-% 3600 University City Science Center
-% Philadelphia, PA 19104-2688
-% USA
-% Telephone: (215) 382-9800
-% Fax: (215) 386-7999
-% e-mail: gray@siam.org
-
-
-% This file is to be used as an example for style only. It should not be read
-% for content.
-
-%%%%%%%%%%%%%%% PLEASE NOTE THE FOLLOWING STYLE RESTRICTIONS %%%%%%%%%%%%%%%
-
-%% 1. There are no new tags. Existing LaTeX tags have been formatted to match
-%% the Preprint series style.
-%%
-%% 2. You must use \cite in the text to mark your reference citations and
-%% \bibitem in the listing of references at the end of your chapter. See
-%% the examples in the following file. If you are using BibTeX, please
-%% supply the bst file with the manuscript file.
-%%
-%% 3. Unless otherwise stated by your editor, do your chapter as if it
-%% is Chapter 1.
-%% If you know which number your chapter is, you must do the following:
-%%
-%% Use the \setcounter command to set the counters for chapter,
-%% section, and page number to the appropriate number. The counter
-%% for chapter is incremental, so it should be set one less than
-%% the actual chapter number. The section counter is not
-%% incremental. Set the page counter to 1. The following example
-%% is set up as if it were chapter 3. Please note the placement of
-%% the three \setcounter commands and follow it exactly.
-%%
-%% 4. This macro is set up for two levels of headings (\section and
-%% \subsection). The macro will automatically number the headings for you.
-%%
-%% 5. The running heads are defined by the \markboth command. The left running
-%% head (the first field of the \markboth command) should be defined with
-%% the authors names. The right running head (the second field of the
-%% \markboth command) should be defined with the title (or shortened title)
-%% of your chapter. Neither running head may be more than 40 characters.
-%%
-%% 6. Theorems, Lemmas, Definitions, etc. are to be triple numbered,
-%% indicating the chapter, section, and the occurence of that element
-%% within that section. (For example, the first theorem in the second
-%% section of chapter three would be numbered 3.2.1. The macro will
-%% automatically do the numbering for you.
-%%
-%% 7. Figures, equations, and tables must be double-numbered indicating
-%% chapter and occurence. Use existing LaTeX tags for these elements.
-%% Numbering will be done automatically.
-%%
-%%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-
-
-\documentstyle[twoside,leqno,twocolumn,ltexpprt]{article}
-
-\begin{document}
-
-
-%\setcounter{chapter}{2} % If you are doing your chapter as chapter one,
-%\setcounter{section}{3} % comment these two lines out.
-
-\title{\large\bf Chapter 1 \\
-\Large SIAM/ACM Preprint Series Macros for
-Use With LaTeX\thanks{Supported by GSF grants ABC123, DEF456, and GHI789.}}
-\author{Corey Gray\thanks{Society for Industrial and Applied Mathematics.} \\
-\and
-Tricia Manning\thanks{Society for Industrial and Applied Mathematics.}}
-\date{}
-
-\maketitle
-
-\pagestyle{myheadings}
-\markboth{AUTHORS NAMES}{CHAPTER TITLE}
-
-%\pagenumbering{arabic}
-%\setcounter{page}{1}%Leave this line commented out.
-
-\begin{abstract} \small\baselineskip=9pt This is the text of my abstract. It is a brief
-description of my
-paper, outlining the purposes and goals I am trying to address.\end{abstract}
-
-\section{Problem Specification.}In this paper, we consider the solution of the $N \times
-N$ linear
-system
-\begin{equation} \label{e1.1}
-A x = b
-\end{equation}
-where $A$ is large, sparse, symmetric, and positive definite. We consider
-the direct solution of (\ref{e1.1}) by means of general sparse Gaussian
-elimination. In such a procedure, we find a permutation matrix $P$, and
-compute the decomposition
-\[
-P A P^{t} = L D L^{t}
-\]
-where $L$ is unit lower triangular and $D$ is diagonal.
-
-
-\section{Design Considerations.}Several good ordering algorithms (nested dissection and
-minimum degree)
-are available for computing $P$ \cite{GEORGELIU}, \cite{ROSE72}.
-Since our interest here does not
-focus directly on the ordering, we assume for convenience that $P=I$,
-or that $A$ has been preordered to reflect an appropriate choice of $P$.
-
-Our purpose here is to examine the nonnumerical complexity of the
-sparse elimination algorithm given in \cite{BANKSMITH}.
-As was shown there, a general sparse elimination scheme based on the
-bordering algorithm requires less storage for pointers and
-row/column indices than more traditional implementations of general
-sparse elimination. This is accomplished by exploiting the m-tree,
-a particular spanning tree for the graph of the filled-in matrix.
-
-\begin{theorem} The method was extended to three
-dimensions. For the standard multigrid
-coarsening
-(in which, for a given grid, the next coarser grid has $1/8$
-as many points), anisotropic problems require plane
-relaxation to
-obtain a good smoothing factor.\end{theorem}
-
-Our purpose here is to examine the nonnumerical complexity of the
-sparse elimination algorithm given in \cite{BANKSMITH}.
-As was shown there, a general sparse elimination scheme based on the
-bordering algorithm requires less storage for pointers and
-row/column indices than more traditional implementations of general
-sparse elimination. This is accomplished by exploiting the m-tree,
-a particular spanning tree for the graph of the filled-in matrix.
-Several good ordering algorithms (nested dissection and minimum degree)
-are available for computing $P$ \cite{GEORGELIU}, \cite{ROSE72}.
-Since our interest here does not
-focus directly on the ordering, we assume for convenience that $P=I$,
-or that $A$ has been preordered to reflect an appropriate choice of $P$.
-
-\begin{proof} In this paper we consider two methods. The first method
-is
-basically the method considered with two differences:
-first, we perform plane relaxation by a two-dimensional
-multigrid method, and second, we use a slightly different
-choice of
-interpolation operator, which improves performance
-for nearly singular problems. In the second method coarsening
-is done by successively coarsening in each of the three
-independent variables and then ignoring the intermediate
-grids; this artifice simplifies coding considerably.
-\end{proof}
-
-Our purpose here is to examine the nonnumerical complexity of the
-sparse elimination algorithm given in \cite{BANKSMITH}.
-As was shown there, a general sparse elimination scheme based on the
-bordering algorithm requires less storage for pointers and
-row/column indices than more traditional implementations of general
-sparse elimination. This is accomplished by exploiting the m-tree,
-a particular spanning tree for the graph of the filled-in matrix.
-
-\begin{Definition}{\rm We describe the two methods in \S 1.2. In \S\ 1.3. we
-discuss
-some remaining details.}
-\end{Definition}
-
-Our purpose here is to examine the nonnumerical complexity of the
-sparse elimination algorithm given in \cite{BANKSMITH}.
-As was shown there, a general sparse elimination scheme based on the
-bordering algorithm requires less storage for pointers and
-row/column indices than more traditional implementations of general
-sparse elimination. This is accomplished by exploiting the m-tree,
-a particular spanning tree for the graph of the filled-in matrix.
-Several good ordering algorithms (nested dissection and minimum degree)
-are available for computing $P$ \cite{GEORGELIU}, \cite{ROSE72}.
-Since our interest here does not
-focus directly on the ordering, we assume for convenience that $P=I$,
-or that $A$ has been preordered to reflect an appropriate choice of $P$.
-
-Our purpose here is to examine the nonnumerical complexity of the
-sparse elimination algorithm given in \cite{BANKSMITH}.
-As was shown there, a general sparse elimination scheme based on the
-bordering algorithm requires less storage for pointers and
-row/column indices than more traditional implementations of general
-sparse elimination.
-
-\begin{lemma} We discuss first the choice for $I_{k-1}^k$
-which is a generalization. We assume that $G^{k-1}$ is
-obtained
-from $G^k$
-by standard coarsening; that is, if $G^k$ is a tensor product
-grid $G_{x}^k \times G_{y}^k \times G_{z}^k$,
-$G^{k-1}=G_{x}^{k-1} \times G_{y}^{k-1} \times G_{z}^{k-1}$,
-where $G_{x}^{k-1}$ is obtained by deleting every other grid
-point of $G_x^k$ and similarly for $G_{y}^k$ and $G_{z}^k$.
-\end{lemma}
-
-To our knowledge, the m-tree previously has not been applied in this
-fashion to the numerical factorization, but it has been used,
-directly or indirectly, in several optimal order algorithms for
-computing the fill-in during the symbolic factorization phase
-[4] - [10], [5], [6]. In \S 1.3., we analyze the complexity of the old and new
-approaches to the intersection problem for the special case of
-an $n \times n$ grid ordered by nested dissection. The special
-structure of this problem allows us to make exact estimates of
-the complexity. To our knowledge, the m-tree previously has not been applied in this
-fashion to the numerical factorization, but it has been used,
-directly or indirectly, in several optimal order algorithms for
-computing the fill-in during the symbolic factorization phase
-[4] - [10], [5], [6].
-
-In \S 1.2, we review the bordering algorithm, and introduce
-the sorting and intersection problems that arise in the
-sparse formulation of the algorithm.
-In \S 1.3., we analyze the complexity of the old and new
-approaches to the intersection problem for the special case of
-an $n \times n$ grid ordered by nested dissection. The special
-structure of this problem allows us to make exact estimates of
-the complexity. To our knowledge, the m-tree previously has not been applied in this
-fashion to the numerical factorization, but it has been used,
-directly or indirectly, in several optimal order algorithms for
-computing the fill-in during the symbolic factorization phase
-[4] - [10], [5], [6].
-
-
-For the old approach, we show that the
-complexity of the intersection problem is $O(n^{3})$, the same
-as the complexity of the numerical computations. For the
-new approach, the complexity of the second part is reduced to
-$O(n^{2} (\log n)^{2})$.
-
-To our knowledge, the m-tree previously has not been applied in this
-fashion to the numerical factorization, but it has been used,
-directly or indirectly, in several optimal order algorithms for
-computing the fill-in during the symbolic factorization phase
-[4] - [10], [5], [6]. In \S 1.3., we analyze the complexity of the old and new
-approaches to the intersection problem for the special case of
-an $n \times n$ grid ordered by nested dissection. The special
-structure of this problem allows us to make exact estimates of
-the complexity. To our knowledge, the m-tree previously has not been applied in this
-fashion to the numerical factorization, but it has been used,
-directly or indirectly, in several optimal order algorithms for
-computing the fill-in during the symbolic factorization phase
-[4] - [10], [5], [6].
-This is accomplished by exploiting the m-tree,
-a particular spanning tree for the graph of the filled-in matrix.
-To our knowledge, the m-tree previously has not been applied in this
-fashion to the numerical factorization, but it has been used,
-directly or indirectly, in several optimal order algorithms for
-computing the fill-in during the symbolic factorization phase
-\cite{EISENSTAT} - \cite{LIU2}, \cite{ROSE76}, \cite{SCHREIBER}.
-
-\subsection{Robustness.}\ We do not
-attempt to present an overview
-here, but rather attempt to focus on those results that
-are relevant to our particular algorithm.
-This section assumes prior knowledge of the role of graph theory
-in sparse Gaussian elimination; surveys of this role are
-available in \cite{ROSE72} and \cite{GEORGELIU}. More general
-discussions of elimination trees are given in
-\cite{LAW} - \cite{LIU2}, \cite{SCHREIBER}.
-Thus, at the $k$th stage, the bordering algorithm consists of
-solving the lower triangular system
-\begin{equation} \label{1.2}
- L_{k-1}v = c
-\end{equation}
-and setting
-\begin{eqnarray}
-\ell &=& D^{-1}_{k-1}v , \\
-\delta &=& \alpha - \ell^{t} v .
-\end{eqnarray}
-
-\begin{figure}
-\vspace{14pc}
-\caption{This is a figure 1.1.}
-\end{figure}
-
-\section{Robustness.} We do not
-attempt to present an overview
-here, but rather attempt to focus on those results that
-are relevant to our particular algorithm.
-
-\subsection{Versatility.}\ The special
-structure of this problem allows us to make exact estimates of
-the complexity. For the old approach, we show that the
-complexity of the intersection problem is $O(n^{3})$, the same
-as the complexity of the numerical computations
-\cite{GEORGELIU}, \cite{ROSEWHITTEN}. For the
-new approach, the complexity of the second part is reduced to
-$O(n^{2} (\log n)^{2})$.
-
-To our knowledge, the m-tree previously has not been applied in this
-fashion to the numerical factorization, but it has been used,
-directly or indirectly, in several optimal order algorithms for
-computing the fill-in during the symbolic factorization phase
-[4] - [10], [5], [6]. In \S 1.3., we analyze the complexity of the old and new
-approaches to the intersection problem for the special case of
-an $n \times n$ grid ordered by nested dissection. The special
-structure of this problem allows us to make exact estimates of
-the complexity. To our knowledge, the m-tree previously has not been applied in this
-fashion to the numerical factorization, but it has been used,
-directly or indirectly, in several optimal order algorithms for
-computing the fill-in during the symbolic factorization phase
-[4] - [10], [5], [6].
-
-In \S 1.2, we review the bordering algorithm, and introduce
-the sorting and intersection problems that arise in the
-sparse formulation of the algorithm.
-In \S 1.3., we analyze the complexity of the old and new
-approaches to the intersection problem for the special case of
-an $n \times n$ grid ordered by nested dissection. The special
-structure of this problem allows us to make exact estimates of
-the complexity. To our knowledge, the m-tree previously has not been applied in this
-fashion to the numerical factorization, but it has been used,
-directly or indirectly, in several optimal order algorithms for
-computing the fill-in during the symbolic factorization phase
-[4] - [10], [5], [6].
-
-
-For the old approach, we show that the
-complexity of the intersection problem is $O(n^{3})$, the same
-as the complexity of the numerical computations. For the
-new approach, the complexity of the second part is reduced to
-$O(n^{2} (\log n)^{2})$.
-
-To our knowledge, the m-tree previously has not been applied in this
-fashion to the numerical factorization, but it has been used,
-directly or indirectly, in several optimal order algorithms for
-computing the fill-in during the symbolic factorization phase
-[4] - [10], [5], [6]. In \S 1.3., we analyze the complexity of the old and new
-approaches to the intersection problem for the special case of
-an $n \times n$ grid ordered by nested dissection. The special
-structure of this problem allows us to make exact estimates of
-the complexity. To our knowledge, the m-tree previously has not been applied in this
-fashion to the numerical factorization, but it has been used,
-directly or indirectly, in several optimal order algorithms for
-computing the fill-in during the symbolic factorization phase
-[4] - [10], [5], [6].
-This is accomplished by exploiting the m-tree,
-a particular spanning tree for the graph of the filled-in matrix.
-To our knowledge, the m-tree previously has not been applied in this
-fashion to the numerical factorization, but it has been used,
-directly or indirectly, in several optimal order algorithms for
-computing the fill-in during the symbolic factorization phase
-\cite{EISENSTAT} - \cite{LIU2}, \cite{ROSE76}, \cite{SCHREIBER}.
-
-\begin{thebibliography}{99}
-
-%\bibitem{GUIDE}
-%R.~E. Bank, {\em PLTMG users' guide, edition 5.0}, tech. report,
-% Department of Mathematics, University of California, San Diego, CA, 1988.
-
-%\bibitem{HBMG}
-%R.~E. Bank, T.~F. Dupont, and H.~Yserentant, {\em The hierarchical basis
-% multigrid method}, Numer. Math., 52 (1988), pp.~427--458.
-
-\bibitem{BANKSMITH}
-R.~E. Bank and R.~K. Smith, {\em General sparse elimination requires no
- permanent integer storage}, SIAM J. Sci. Stat. Comput., 8 (1987),
- pp.~574--584.
-
-\bibitem{EISENSTAT}
-S.~C. Eisenstat, M.~C. Gursky, M.~Schultz, and A.~Sherman, {\em
- Algorithms and data structures for sparse symmetric gaussian elimination},
- SIAM J. Sci. Stat. Comput., 2 (1982), pp.~225--237.
-
-\bibitem{GEORGELIU}
-A.~George and J.~Liu, {\em Computer Solution of Large Sparse Positive
- Definite Systems}, Prentice Hall, Englewood Cliffs, NJ, 1981.
-
-\bibitem{LAW}
-K.~H. Law and S.~J. Fenves, {\em A node addition model for symbolic
- factorization}, ACM TOMS, 12 (1986), pp.~37--50.
-
-\bibitem{LIU}
-J.~W.~H. Liu, {\em A compact row storage scheme for cholesky factors
- using elimination trees}, ACM TOMS, 12 (1986), pp.~127--148.
-
-\bibitem{LIU2}
-\sameauthor , {\em The role of
- elimination trees in sparse factorization}, Tech. Report CS-87-12,Department
- of Computer Science, York University, Ontario, Canada, 1987.
-
-\bibitem{ROSE72}
-D.~J. Rose, {\em A graph theoretic study of the numeric solution of
- sparse positive definite systems}, in Graph Theory and Computing, AcademicΠPress, New
-York, 1972.
-
-\bibitem{ROSE76}
-D.~J. Rose, R.~E. Tarjan, and G.~S. Lueker, {\em Algorithmic aspects of
- vertex elimination on graphs}, SIAM J. Comput., 5 (1976), pp.~226--283.
-
-\bibitem{ROSEWHITTEN}
-D.~J. Rose and G.~F. Whitten, {\em A recursive analysis of disection
- strategies}, in Sparse Matrix Computations, Academic Press, New York, 1976.
-
-\bibitem{SCHREIBER}
-R.~Schrieber, {\em A new implementation of sparse gaussian elimination},
- ACM TOMS, 8 (1982), pp.~256--276.
-
-\end{thebibliography}
-\end{document}
-
-% End of ltexpprt.tex
-%
-%
-%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% CUT HERE %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%
-%
-%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% ltexpprt.sty %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%
-% This is ltexpprt.sty, a file of macros and definitions for creating a
-% chapter for publication in the ACM/SIAM Preprint series using LaTeX.
-% It is designed to produce double-column output.
-% This file may be freely distributed but may not be altered in any way.
-% Any comments or questions regarding these macros should be directed to:
-
-% Corey Gray
-% SIAM
-% 3600 University City Science Center
-% Philadelphia, PA 19104-2688
-% USA
-% Telephone: (215) 382-9800
-% Fax: (215) 386-7999
-% e-mail: gray@siam.org
-
-
-% Report the version.
-\message{*** ACM/SIAM LaTeX Preprint Series macro package, version 1.0,
-September 24,1990 ***}
-
-
-\pretolerance=800
-\tolerance=10000
-\sloppy
-
-\voffset=-.5in
-\hoffset=-.5in
-\vsize=55pc
-\hsize=41pc
-\baselineskip=14pt
-\footskip=18pt
-\topmargin 24pt
-\headheight 12pt
-\headsep 17pt
-\textheight 52.5pc \advance\textheight by \topskip
-\textwidth 41pc
-\parskip 0pt
-\parindent 18pt
-
-\font\tensmc=cmcsc10
-\def\smc{\tensmc}
-
-%% footnotes to be set 8/10
-\def\footnotesize{\@setsize\footnotesize{10pt}\viiipt\@viiipt
- % \indent
- \abovedisplayskip \z@
- \belowdisplayskip\z@
- \abovedisplayshortskip\abovedisplayskip
- \belowdisplayshortskip\belowdisplayshortskip
- \def\@listi{\leftmargin\leftmargini \topsep 3pt plus 1pt minus 1pt
- \parsep 2pt plus 1pt minus 1pt
- \itemsep \parsep}}
-
-\let\referencesize\footnotesize
-
-\footnotesep 0pt
-
-\skip\footins 12pt plus 12pt
-
-\def\footnoterule{\kern3\p@ \hrule width 3em} % the \hrule is .4pt high
-
-\def\ps@plain{\let\@mkboth\@gobbletwo
- \def\@oddfoot{{\hfil\small\thepage\hfil}}%
- \def\@oddhead{}
- \def\@evenhead{}\def\@evenfoot{}}
-
-
-
-
-
-\def\ps@headings{\let\@mkboth\markboth
- \def\@oddfoot{}\def\@evenfoot{}%
- \def\@evenhead{{\rm\thepage}\hfil{\small\leftmark}}%
- \def\@oddhead{{\noindent\small\rightmark}\hfil{\rm\thepage}}%
-
-
-
-\def\ps@myheadings{\let\@mkboth\@gobbletwo
- \def\@oddfoot{}\def\@evenfoot{}%
- \def\@oddhead{\rlap{\normalsize\rm\rightmark}\hfil{small\thepage}}%
- \def\@evenhead%{\hfil{\small\@chapapp}\
- {\small\thepage}\hfil\llap{\normalsize\rm\leftmark}}%
- \def\chaptermark##1{}%
- \def\sectionmark##1{}\def\subsectionmark##1{}}
-
-
-\def\theequation{\arabic{section}.\arabic{equation}}
-
-
-\def\section{\@startsection{section}{1}{0pt}{-12pt}{3pt}{\hyphenpenalty=\@M
-\exhyphenpenalty=\@M\normalsize\bf}}
-\def\subsection{\@startsection{subsection}{2}{0pt}{-12pt}{0pt}{\normalsize\bf}
-}
-\def\subsubsection{\@startsection
- {subsubsection}{3}{0pt}{-12pt}{0pt}{\normalsize\bf}}
-\def\paragraph{\@startsection
- {paragraph}{4}{\parindent}{0pt}{0pt}{\normalsize\bf}}
-\def\subparagraph{\@startsection
- {subparagraph}{4}{\parindent}{0pt}{0pt}{\normalsize\bf}}
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% %
-% THEOREMS, PROOFS, ALGORITHMS %
-% %
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-%%% defined proof environment by theorem model (took out counter)
-
-\def\newproof#1{\@nprf{#1}}
-
-\def\@nprf#1#2{\@xnprf{#1}{#2}}
-
-\def\@xnprf#1#2{\expandafter\@ifdefinable\csname #1\endcsname
-\global\@namedef{#1}{\@prf{#1}{#2}}\global\@namedef{end#1}{\@endproof}}
-
-\def\@prf#1#2{\@xprf{#1}{#2}}
-
-\def\@xprf#1#2{\@beginproof{#2}{\csname the#1\endcsname}\ignorespaces}
-
-
-
-%%% defined algorithm environment by theorem model
-
-\def\newalgorithm#1{\@ifnextchar[{\@oalg{#1}}{\@nalg{#1}}}
-
-\def\@nalg#1#2{%
-\@ifnextchar[{\@xnalg{#1}{#2}}{\@ynalg{#1}{#2}}}
-
-\def\@xnalg#1#2[#3]{\expandafter\@ifdefinable\csname #1\endcsname
-{\@definecounter{#1}\@addtoreset{#1}{#3}%
-\expandafter\xdef\csname the#1\endcsname{\expandafter\noexpand
- \csname the#3\endcsname \@thmcountersep \@thmcounter{#1}}%
-\global\@namedef{#1}{\@alg{#1}{#2}}\global\@namedef{end#1}{\@endalgorithm}}}
-
-\def\@ynalg#1#2{\expandafter\@ifdefinable\csname #1\endcsname
-{\@definecounter{#1}%
-\expandafter\xdef\csname the#1\endcsname{\@thmcounter{#1}}%
-\global\@namedef{#1}{\@alg{#1}{#2}}\global\@namedef{end#1}{\@endalgorithm}}}
-
-\def\@oalg#1[#2]#3{\expandafter\@ifdefinable\csname #1\endcsname
- {\global\@namedef{the#1}{\@nameuse{the#2}}%
-\global\@namedef{#1}{\@alg{#2}{#3}}%
-\global\@namedef{end#1}{\@endalgorithm}}}
-
-\def\@alg#1#2{\refstepcounter
- {#1}\@ifnextchar[{\@yalg{#1}{#2}}{\@xalg{#1}{#2}}}
-
-\def\@xalg#1#2{\@beginalgorithm{#2}{\csname the#1\endcsname}\ignorespaces}
-\def\@yalg#1#2[#3]{\@opargbeginalgorithm{#2}{\csname
- the#1\endcsname}{#3}\ignorespaces}
-
-
-
-
-\def\@beginproof#1{\rm \trivlist \item[\hskip \labelsep{\it #1.\/}]}
-\def\@endproof{\outerparskip 0pt\endtrivlist}
-
-\def\@begintheorem#1#2{\it \trivlist \item[\hskip \labelsep{\sc #1\ #2.}]}
-\def\@opargbegintheorem#1#2#3{\it \trivlist
- \item[\hskip \labelsep{\sc #1\ #2.\ (#3)}]}
-\def\@endtheorem{\outerparskip 0pt\endtrivlist}
-
-%\def\@begindefinition#1#2{\rm \trivlist \item[\hskip \labelsep{\sc #1\ #2.}]}
-%\def\@opargbegindefinition#1#2#3{\rm \trivlist
-% \item[\hskip \labelsep{\sc #1\ #2.\ (#3)}]}
-%\def\@enddefinition{\outerparskip 0pt\endtrivlist}
-
-
-\def\@beginalgorithm#1#2{\rm \trivlist \item[\hskip \labelsep{\sc #1\ #2.}]}
-\def\@opargbeginalgorithm#1#2#3{\rm \trivlist
- \item[\hskip \labelsep{\sc #1\ #2.\ (#3)}]}
-\def\@endalgorithm{\outerparskip 6pt\endtrivlist}
-
-
-\newskip\outerparskip
-
-\def\trivlist{\parsep\outerparskip
- \@trivlist \labelwidth\z@ \leftmargin\z@
- \itemindent\parindent \def\makelabel##1{##1}}
-
-\def\@trivlist{\topsep=0pt\@topsepadd\topsep
- \if@noskipsec \leavevmode \fi
- \ifvmode \advance\@topsepadd\partopsep \else \unskip\par\fi
- \if@inlabel \@noparitemtrue \@noparlisttrue
- \else \@noparlistfalse \@topsep\@topsepadd \fi
- \advance\@topsep \parskip
- \leftskip\z@\rightskip\@rightskip \parfillskip\@flushglue
- \@setpar{\if@newlist\else{\@@par}\fi}%
- \global\@newlisttrue \@outerparskip\parskip}
-
-
-\def\endtrivlist{\if@newlist\@noitemerr\fi
- \if@inlabel\indent\fi
- \ifhmode\unskip \par\fi
- \if@noparlist \else
- \ifdim\lastskip >\z@ \@tempskipa\lastskip \vskip -\lastskip
- \advance\@tempskipa\parskip \advance\@tempskipa -\@outerparskip
- \vskip\@tempskipa
- \fi\@endparenv\fi
- \vskip\outerparskip}
-
-
-
- \newproof{@proof}{Proof}
- \newenvironment{proof}{\begin{@proof}}{\end{@proof}}
-
- \newtheorem{@theorem}{Theorem}[section]
- \newenvironment{theorem}{\begin{@theorem}}{\end{@theorem}}
-
- \newalgorithm{@algorithm}{Algorithm}[section]
- \newenvironment{algorithm}{\begin{@algorithm}}{\end{@algorithm}}
-
-
-
-\newtheorem{lemma}{Lemma}[section]
-\newtheorem{fact}{Fact}[section]
-\newtheorem{corollary}{Corollary}[section]
-\newtheorem{axiom}{Axiom}[section]
-\newtheorem{cond}{Condition}[section]
-\newtheorem{property}{Property}[section]
-\newtheorem{proposition}{Proposition}[section]
-
-\newtheorem{Conjecture}{Conjecture}[section]
-%\newtheorem{Corollary}[Theorem]{Corollary}
-\newtheorem{Definition}{Definition}[section]
-\newtheorem{Lemma}{Lemma}[section]
-\newtheorem{Remark}{Remark}[section]
-
-\newproof{Example}{Example}
-\newproof{Method}{Method}
-\newproof{Exercise}{Exercise}
-
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% %%
-%% BIBLIOGRAPHY %%
-%% %%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-
-\def\thebibliography#1{%
-%\cleardoublepage
-\parindent 0em
-\vspace{6pt}
-\begin{flushleft}\normalsize\bf References\end{flushleft}
-\addvspace{3pt}\nopagebreak\list
- %% default is no labels, for those not using \cite or BibTeX
-% {[\arabic{enumi}]} {\settowidth\labelwidth{[#1]}
-{[\arabic{enumi}]}{\settowidth\labelwidth{mm}
-\leftmargin\labelwidth
- \advance\leftmargin\labelsep
- \usecounter{enumi}\@bibsetup}
-\def\newblock{\hskip .11em plus .33em minus -.07em}
- \sloppy\clubpenalty4000\widowpenalty4000
- \sfcode`\.=1000\relax}
-
-%% setup 8/10 type
-\def\@bibsetup{\itemindent=0pt \itemsep=0pt \parsep=0pt
-\small}
-
-\def\sameauthor{\leavevmode\vrule height 2pt depth -1.6pt width 23pt}
-
-%
-%% End of ltexpprt.sty
-%
-%%%%%%%%%%%%%%%%%%%%%%%%% End of ltexpprt.all %%%%%%%%%%%%%%%%%%%%%%%
- \ No newline at end of file
diff --git a/Master/texmf-dist/source/latex/siam/ltexproc.all b/Master/texmf-dist/source/latex/siam/ltexproc.all
deleted file mode 100644
index 61283eec0aa..00000000000
--- a/Master/texmf-dist/source/latex/siam/ltexproc.all
+++ /dev/null
@@ -1,1784 +0,0 @@
-
-
-This file constitutes the full distribution for SIAM Proceedings
-Series LaTeX version macros. The files included here are:
-
-ltexproc.tex (An example file, also containing documentation)
-
-ltexproc.sty (The style file)
-
-siamproc.bst (for BiBTeX users)
-
-To use these macros, separate the files at the indicated cut lines.
-
-%%%%%%%%%%%%%%%%%%%%%%%%CUT HERE%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-% This is ltexproc.tex, an example file for use with the SIAM LaTeX
-% Proceedings Series macros.
-% Please take the time to read the following comments, as they describe
-% how to use these macros. This file can be composed and printed out for
-% use as sample output.
-
-% Any comments or questions regarding these macros should be directed to:
-%
-% Corey Gray
-% SIAM
-% 3600 University City Science Center
-% Philadelphia, PA 19104-2688
-% USA
-% Telephone: (215) 382-9800
-% Fax: (215) 386-7999
-% e-mail: gray@siam.org
-
-
-% This file is to be used as an example for style only. It should not be read
-% for content.
-
-%%%%%%%%%%%%%%% PLEASE NOTE THE FOLLOWING STYLE RESTRICTIONS %%%%%%%%%%%%%%%
-
-%% 1. There are no new tags. Existing LaTeX tags have been formatted to
-%% match the Proceedings series style.
-%%
-%% 2. You must use \cite in the text to mark your reference citations and
-%% \bibitem in the listing of references at the end of your chapter. See
-%% the examples in the following file. The file siamproc.bst has been
-%% included for use with BiBTeX. Please be sure to include the appropriate
-%% .bib file with BiBTeX submissions. You may also submit the .bbl file
-%% instead of the .bib file.
-%%
-%% 3. Unless otherwise stated by your editor, do your chapter as if it
-%% is Chapter 1. The appropriate chapter number will be included during
-%% the production of the proceedings.
-%%
-%% 4. This macro is set up for three levels of headings (\section,
-%% \subsection, and \subsubsection). The macro will automatically number
-%% the headings for you.
-%%
-%% 5. The running heads are indicated by the \markboth command. Please
-%% define the running heads by placing the authors last names in the
-%% first field and the title of the paper in the second field.
-%% They should be typed initial cap and lower case. Please see the example.
-%% Neither field can contain more than 50 characters including spaces,
-%% so please use a shortened version of the title if necessary. For
-%% papers with multiple authors please follow these rules; for
-%% two authors type {Author 1 and Author 2}; for more that two authors type
-%% {Author 1 et al.}.
-%%
-%% 6. Theorems, Lemmas, Definitions, etc. are to be double-numbered,
-%% indicating the section and the occurrence of that element
-%% within that section. (For example, the first theorem in the second
-%% section would be numbered 2.1. The macro will
-%% automatically do the numbering for you.
-%%
-%% 7. Proofs are handled with the commands \begin{proof}\end{proof}.
-%% If you wish to use an end of proof box, use \qed preceding \end{proof}.
-%% The example uses one. It is not required.
-%%
-%% 8. Figures, equations, and tables must be single-numbered. All equation
-%% numbers are to be on the left. Figure captions should be placed under
-%% the figures they pertain to. Table captions should be placed above
-%% the tables. Use existing LaTeX tags for these elements. Numbering of
-%% these elements will be done automatically. SIAM supports the use of
-%% psfig for including Postscript figures. All Postscript figures should be
-%% sent as separate files. A hardcopy version of all Postscript figures
-%% is also required. See note regarding this under How to Submit Your Paper.
-%%
-%% 9. Grant information and author affiliations.
-%% This information is included in the file with the two commands,
-%% \thanks and \footnotemark []. (See example). The \thanks command
-%% produces a footnote for the title or author, and places the
-%% appropriate footnote symbol with the title or author and at the
-%% bottom of the page. The \footnotemark [] command allows the use of
-%% duplicate footnote symbols. This macro follows the normal LaTeX order
-%% of footnote symbols. Below is a list of these symbols, and their
-%% corresponding footnotemark:
-%%
-%% asterisk \footnotemark[1]
-%% single-dagger \footnotemark[2]
-%% double-dagger \footnotemark[3]
-%% section sign \footnotemark[4]
-%% paragraph \footnotemark[5]
-%% parallel \footnotemark[6]
-%% double asterisk \footnotemark[7]
-%% double single-dagger \footnotemark[8]
-%% double double-dagger \footnotemark[9]
-%%
-%% The following general rules for grants and affiliations apply:
-%% a) If there is a single grant for the paper, then the grant
-%% information should be footnoted to the title.
-%% b) If there is more than one grant, include the grant information
-%% with each author's affiliation.
-%% c) If there are different grants for the paper but the authors share
-%% the same affiliation, footnote the grant information to the title.
-%% For example, The work of the first author was supported by xyz.
-%% The work of the second author was supported by abc. And so on.
-%% d) For authors sharing the same affiliation, use \thanks for the
-%% first author with that affiliation and the appropriate
-%% \footnotemark[] (from the list above) for all subsequent authors
-%% with that affiliation.
-%%
-%% 10. Special fonts.
-%% SIAM supports the use of AMS-TeX fonts version 2.0 and later. As
-%% described in the manual for these fonts, they can be included by
-%% \input{amssym.def} and \input{amssym.tex}. These macros are not yet
-%% updated to make use of the New Font Selection Scheme (NFSS) of
-%% Mittelbach and Schopf. To make these macros compatible with NFSS, use
-%% the oldlfont style option.
-%%
-%% 11. How to Submit Your Paper.
-%% The electronic version of your paper should be sent to proceed@siam.org.
-%% A hardcopy version should also be submitted. Instructions are included
-%% in your acceptance letter. Please be sure to send hardcopy
-%% versions of any Postscript figures you have submitted electronically.
-%% Be sure to return your signed Copyright Transfer Agreement. We cannot
-%% publish your paper without it.
-%%
-%%
-%%
-%%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%-
-%%%
-
-
-\documentstyle[leqno,twoside,11pt,ltexproc]{article} %You must set up your
- %\documentstyle line like this.
-
-
-\begin{document}
-\cleardoublepage
-\pagestyle{myheadings}
-
-\title{Chapter 1\\
-SIAM Proceedings Series Macros\\
- for Use With LaTeX\thanks{Any information regarding grants should be placed
-here.}}
-\author{J. Corey Gray\thanks{Production Manager, Society for Industrial and Applied
-Mathematics, Philadelphia, PA.}
-\and
-Tricia Manning\thanks{Publications Specialist, Society for Industrial and Applied
-Mathematics, Philadelphia, PA.}
-\and
-Vickie Kearn\thanks{Publisher, Society for Industrial and Applied Mathematics,
-Philadelphia, PA.}\\
-\and
-Nancy Abbott\thanks{Design Supervisor, Society for Industrial and Applied
-Mathematics, Philadelphia, PA}
-\and
-Sue Ciambrano\thanks{Acquisitions Editor, Society for Industrial and Applied
-Mathematics, Philadelphia, PA}
-\and
-Paul Duggan\thanks{Composition Specialist, Society for Industrial and Applied
-Mathematics, Philadelphia, PA}
-\and
-Robbi Anne Albert\thanks{Production Assistant, Society for Industrial and Applied
-Mathematics, Philadelphia, PA}
-\and
-Jean Anderson\thanks{Composition Coordinator, Society for Industrial and Applied
-Mathematics, Philadelphia, PA}
-}
-\date{}
-\maketitle
-\markboth{Gray et al.}{SIAM Proceedings Series Macros} % See section 5 above
- % for explanation.
-\pagenumbering{arabic}
-
-\begin{abstract}An equivalence is shown between realizability of input/output (i/o) operators by
-rational control systems and high-order algebraic differential equations for
-i/o pairs. This generalizes, to nonlinear systems, the equivalence
-between autoregressive representations and finite dimensional linear
-realizability. \end{abstract}
-\section{Problem Specification}In this paper, we consider the solution of the $N \times
-N$ linear
-system
-\begin{equation} \label{e1.1}
-\cos \sin A x = b
-\end{equation}
-where $A$ is large, sparse, symmetric, and positive definite. We consider
-the direct solution of (\ref{e1.1}) by means of general sparse Gaussian
-elimination. In such a procedure, we find a permutation matrix $P$, and
-compute the decomposition
-\[
-P A P^{t} = L D L^{t}
-\]
-where $L$ is unit lower triangular and $D$ is diagonal.
-
-
-\section{Design Considerations}Several good ordering algorithms (nested dissection and
-minimum degree)
-are available for computing $P$ \cite{GEORGELIU}, \cite{ROSE72}.
-Since our interest here does not
-focus directly on the ordering, we assume for convenience that $P=I$,
-or that $A$ has been preordered to reflect an appropriate choice of $P$.
-
-Our purpose here is to examine the nonnumerical complexity of the
-sparse elimination algorithm given in \cite{BANKSMITH}.
-As was shown there, a general sparse elimination scheme based on the
-bordering algorithm requires less storage for pointers and
-row/column indices than more traditional implementations of general
-sparse elimination. This is accomplished by exploiting the m-tree,
-a particular spanning tree for the graph of the filled-in matrix.
-
-\begin{theorem} The method was extended to three
-dimensions. For the standard multigrid
-coarsening
-(in which, for a given grid, the next coarser grid has $1/8$
-as many points), anisotropic problems require plane
-relaxation to
-obtain a good smoothing factor.\end{theorem}
-
-Several good ordering algorithms (nested dissection and minimum degree)
-are available for computing $P$ \cite{GEORGELIU}, \cite{ROSE72}.
-Since our interest here does not
-focus directly on the ordering, we assume for convenience that $P=I$,
-or that $A$ has been preordered to reflect an appropriate choice of $P$.
-
-
-\begin{proof} In this paper we consider two methods. The first method
-is
-basically the method considered with two differences:
-first, we perform plane relaxation by a two-dimensional
-multigrid method, and second, we use a slightly different
-choice of
-interpolation operator, which improves performance
-for nearly singular problems. In the second method coarsening
-is done by successively coarsening in each of the three
-independent variables and then ignoring the intermediate
-grids; this artifice simplifies coding considerably.\qed
-\end{proof}
-
-Our purpose here is to examine the nonnumerical complexity of the
-sparse elimination algorithm given in \cite{BANKSMITH}.
-As was shown there, a general sparse elimination scheme based on the
-bordering algorithm requires less storage for pointers and
-row/column indices than more traditional implementations of general
-sparse elimination. This is accomplished by exploiting the m-tree,
-a particular spanning tree for the graph of the filled-in matrix.
-
-\begin{Definition}{\rm We describe the two methods in \S 1.2. In \S\ 1.3. we
-discuss
-some remaining details.}
-\end{Definition}
-
-\begin{figure}
-\vspace*{24pc}
-\caption{This is figure 1.}
-\end{figure}
-
-Our purpose here is to examine the nonnumerical complexity of the
-sparse elimination algorithm given in \cite{BANKSMITH}.
-As was shown there, a general sparse elimination scheme based on the
-bordering algorithm requires less storage for pointers and
-row/column indices than more traditional implementations of general
-sparse elimination.
-
-\begin{lemma} We discuss first the choice for $I_{k-1}^k$
-which is a generalization. We assume that $G^{k-1}$ is
-obtained
-from $G^k$
-by standard coarsening; that is, if $G^k$ is a tensor product
-grid $G_{x}^k \times G_{y}^k \times G_{z}^k$,
-$G^{k-1}=G_{x}^{k-1} \times G_{y}^{k-1} \times G_{z}^{k-1}$,
-where $G_{x}^{k-1}$ is obtained by deleting every other grid
-point of $G_x^k$ and similarly for $G_{y}^k$ and $G_{z}^k$.
-\end{lemma}
-
-This is accomplished by exploiting the m-tree,
-a particular spanning tree for the graph of the filled-in matrix.
-To our knowledge, the m-tree previously has not been applied in this
-fashion to the numerical factorization, but it has been used,
-directly or indirectly, in several optimal order algorithms for
-computing the fill-in during the symbolic factorization phase
-\cite{EISENSTAT} - \cite{LIU2}, \cite{ROSE76}, \cite{SCHREIBER}.
-
-\subsection{Robustness}
-We do not
-attempt to present an overview
-here, but rather attempt to focus on those results that
-are relevant to our particular algorithm.
-This section assumes prior knowledge of the role of graph theory
-in sparse Gaussian elimination; surveys of this role are
-available in \cite{ROSE72} and \cite{GEORGELIU}. More general
-discussions of elimination trees are given in
-\cite{LAW} - \cite{LIU2}, \cite{SCHREIBER}.
-Thus, at the $k$th stage, the bordering algorithm consists of
-solving the lower triangular system
-\begin{equation} \label{1.2}
- L_{k-1}v = c
-\end{equation}
-and setting
-\begin{eqnarray}
-\ell &=& D^{-1}_{k-1}v , \\
-\delta &=& \alpha - \ell^{t} v .
-\end{eqnarray}
-
-\subsubsection{Versatility.} We do not
-attempt to present an overview
-here, but rather attempt to focus on those results that
-are relevant to our particular algorithm.
-
-\section{Conclusions} The special
-structure of this problem allows us to make exact estimates of
-the complexity. For the old approach, we show that the
-complexity of the intersection problem is $O(n^{3})$, the same
-as the complexity of the numerical computations
-\cite{GEORGELIU}, \cite{ROSEWHITTEN}. For the
-new approach, the complexity of the second part is reduced to
-$O(n^{2} (\log n)^{2})$.
-
-\begin{thebibliography}{99}
-
-
-\bibitem{BANKSMITH}
-R.~E. Bank and R.~K. Smith, {\em General sparse elimination requires no
- permanent integer storage}, SIAM J. Sci. Stat. Comput., 8 (1987),
- pp.~574--584.
-
-\bibitem{EISENSTAT}
-S.~C. Eisenstat, M.~C. Gursky, M.~Schultz, and A.~Sherman, {\em
- Algorithms and data structures for sparse symmetric gaussian elimination},
- SIAM J. Sci. Stat. Comput., 2 (1982), pp.~225--237.
-
-\bibitem{GEORGELIU}
-A.~George and J.~Liu, {\em Computer Solution of Large Sparse Positive
- Definite Systems}, Prentice Hall, Englewood Cliffs, NJ, 1981.
-
-\bibitem{LAW}
-K.~H. Law and S.~J. Fenves, {\em A node addition model for symbolic
- factorization}, ACM TOMS, 12 (1986), pp.~37--50.
-
-\bibitem{LIU}
-J.~W.~H. Liu, {\em A compact row storage scheme for cholesky factors
- using elimination trees}, ACM TOMS, 12 (1986), pp.~127--148.
-
-\bibitem{LIU2}
-\sameauthor , {\em The role of
- elimination trees in sparse factorization}, Tech. Report CS-87-12,Department
- of Computer Science, York University, Ontario, Canada, 1987.
-
-\bibitem{ROSE72}
-D.~J. Rose, {\em A graph theoretic study of the numeric solution of
- sparse positive definite systems}, in Graph Theory and Computing, Academic Press, New
-York, 1972.
-
-\bibitem{ROSE76}
-D.~J. Rose, R.~E. Tarjan, and G.~S. Lueker, {\em Algorithmic aspects of
- vertex elimination on graphs}, SIAM J. Comput., 5 (1976), pp.~226--283.
-
-\bibitem{ROSEWHITTEN}
-D.~J. Rose and G.~F. Whitten, {\em A recursive analysis of disection
- strategies}, in Sparse Matrix Computations, Academic Press, New York, 1976.
-
-\bibitem{SCHREIBER}
-R.~Schreiber, {\em A new implementation of sparse gaussian elimination},
- ACM TOMS, 8 (1982), pp.~256--276.
-
-\end{thebibliography}
-
-\end{document}
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%CUT HERE%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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-% Corey Gray
-% SIAM
-% 3600 University City Science Center
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-{ "" 'last.authors :=
-}
-
-FUNCTION {format.authors}
-{ author empty$
- { "" 'last.authors :=
- ""
- }
- { author last.authors =
- { "\leavevmode\vrule height 2pt depth -1.6pt width 23pt" }
- { author format.names }% scapify }
- if$
- author 'last.authors :=
- }
- if$
-}
-
-FUNCTION {format.organization}
-{ organization empty$
- { "" 'last.authors :=
- ""
- }
- { organization last.authors =
- { "\leavevmode\vrule height 2pt depth -1.6pt width 23pt" }
- { organization scapify }
- if$
- organization 'last.authors :=
- }
- if$
-}
-
-FUNCTION {format.editors}
-{ editor empty$
- { "" 'last.authors :=
- ""
- }
- { editor last.authors =
- { "\leavevmode\vrule height 2pt depth -1.6pt width 23pt" }
- { editor format.names scapify }
- if$
- editor num.names$ #1 >
- { ", eds." * }
- { ", ed." * }
- if$
- editor 'last.authors :=
- }
- if$
-}
-
-FUNCTION {format.ineditors}
-{ editor empty$
- { "" }
- { editor format.names
- editor num.names$ #1 >
- { ", eds." * }
- { ", ed." * }
- if$
- }
- if$
-}
-
-FUNCTION {format.title}
-{ title empty$
- { "" }
- { title "t" change.case$ emphasize }
- if$
-}
-
-FUNCTION {n.dashify}
-{ 't :=
- ""
- { t empty$ not }
- { t #1 #1 substring$ "-" =
- { t #1 #2 substring$ "--" = not
- { "--" *
- t #2 global.max$ substring$ 't :=
- }
- { { t #1 #1 substring$ "-" = }
- { "-" *
- t #2 global.max$ substring$ 't :=
- }
- while$
- }
- if$
- }
- { t #1 #1 substring$ *
- t #2 global.max$ substring$ 't :=
- }
- if$
- }
- while$
-}
-
-FUNCTION {format.date}
-{ year empty$
- { month empty$
- { "" }
- { "there's a month but no year in " cite$ * warning$
- month
- }
- if$
- }
- { month empty$
- 'year
- { month " " * year * }
- if$
- }
- if$
-}
-
-FUNCTION {format.btitle}
-{ title emphasize
-}
-
-FUNCTION {tie.or.space.connect}
-{ duplicate$ text.length$ #3 <
- { "~" }
- { " " }
- if$
- swap$ * *
-}
-
-FUNCTION {either.or.check}
-{ empty$
- 'pop$
- { "can't use both " swap$ * " fields in " * cite$ * warning$ }
- if$
-}
-
-FUNCTION {format.bvolume}
-{ volume empty$
- { "" }
- { "vol.~" volume *
- series empty$
- 'skip$
- { " of " * series * }
- if$
- "volume and number" number either.or.check
- }
- if$
-}
-
-FUNCTION {format.number.series}
-{ volume empty$
- { number empty$
- { series field.or.null }
- { "no.~" number *
- series empty$
- { "there's a number but no series in " cite$ * warning$ }
- { " in " * series * }
- if$
- }
- if$
- }
- { "" }
- if$
-}
-
-FUNCTION {format.edition}
-{ edition empty$
- { "" }
- { edition "l" change.case$ "~ed." * }
- if$
-}
-
-INTEGERS { multiresult }
-
-FUNCTION {multi.page.check}
-{ 't :=
- #0 'multiresult :=
- { multiresult not
- t empty$ not
- and
- }
- { t #1 #1 substring$
- duplicate$ "-" =
- swap$ duplicate$ "," =
- swap$ "+" =
- or or
- { #1 'multiresult := }
- { t #2 global.max$ substring$ 't := }
- if$
- }
- while$
- multiresult
-}
-
-FUNCTION {format.pages}
-{ pages empty$
- { "" }
- { pages multi.page.check
- { "pp.~" pages n.dashify * }
- { "p.~" pages * }
- if$
- }
- if$
-}
-
-FUNCTION {format.vol.year}
-{ volume field.or.null
- year empty$
- { "empty year in " cite$ * warning$ }
- { " (" year * ")" * * }
- if$
-}
-
-FUNCTION {format.chapter.pages}
-{ chapter empty$
- 'format.pages
- { type empty$
- { "ch.~" chapter * }
- { type "l" change.case$ chapter tie.or.space.connect }
- if$
- pages empty$
- 'skip$
- { ", " * format.pages * }
- if$
- }
- if$
-}
-
-FUNCTION {format.in.ed.booktitle}
-{ booktitle empty$
- { "" }
- { editor empty$
- { "in " booktitle * }
- { "in " booktitle * ", " * format.ineditors * }
- if$
- }
- if$
-}
-
-FUNCTION {empty.misc.check}
-{ author empty$ title empty$ howpublished empty$
- month empty$ year empty$ note empty$
- and and and and and
- key empty$ not and
- { "all relevant fields are empty in " cite$ * warning$ }
- 'skip$
- if$
-}
-
-FUNCTION {format.thesis.type}
-{ type empty$
- 'skip$
- { pop$
- type "l" change.case$
- }
- if$
-}
-
-FUNCTION {format.tr.number}
-{ type empty$
- { "Tech. Rep." }
- 'type
- if$
- number empty$
- { "l" change.case$ }
- { number tie.or.space.connect }
- if$
-}
-
-FUNCTION {format.article.crossref}
-{ key empty$
- { journal empty$
- { "need key or journal for " cite$ * " to crossref " * crossref *
- warning$
- ""
- }
- { "in " journal * }
- if$
- }
- { "in " key * }
- if$
- " \cite{" * crossref * "}" *
-}
-
-FUNCTION {format.crossref.editor}
-{ editor #1 "{vv~}{ll}" format.name$
- editor num.names$ duplicate$
- #2 >
- { pop$ " et~al." * }
- { #2 <
- 'skip$
- { editor #2 "{ff }{vv }{ll}{ jj}" format.name$ "others" =
- { " et~al." * }
- { " and " * editor #2 "{vv~}{ll}" format.name$ * }
- if$
- }
- if$
- }
- if$
-}
-
-FUNCTION {format.book.crossref}
-{ volume empty$
- { "empty volume in " cite$ * "'s crossref of " * crossref * warning$
- "in "
- }
- { "vol.~" volume *
- " of " *
- }
- if$
- editor empty$
- editor field.or.null author field.or.null =
- or
- { key empty$
- { series empty$
- { "need editor, key, or series for " cite$ * " to crossref " *
- crossref * warning$
- "" *
- }
- { series * }
- if$
- }
- { key * }
- if$
- }
- { format.crossref.editor * }
- if$
- " \cite{" * crossref * "}" *
-}
-
-FUNCTION {format.incoll.inproc.crossref}
-{ editor empty$
- editor field.or.null author field.or.null =
- or
- { key empty$
- { booktitle empty$
- { "need editor, key, or booktitle for " cite$ * " to crossref " *
- crossref * warning$
- ""
- }
- { "in " booktitle * }
- if$
- }
- { "in " key * }
- if$
- }
- { "in " format.crossref.editor * }
- if$
- " \cite{" * crossref * "}" *
-}
-
-FUNCTION {article}
-{ output.bibitem
- format.authors "author" output.check
- format.title "title" output.check
- crossref missing$
- { journal "journal" output.check
- format.vol.year output
- }
- { format.article.crossref output.nonnull }
- if$
- format.pages output
- new.block
- note output
- fin.entry
-}
-
-FUNCTION {book}
-{ output.bibitem
- author empty$
- { format.editors "author and editor" output.check }
- { format.authors output.nonnull
- crossref missing$
- { "author and editor" editor either.or.check }
- 'skip$
- if$
- }
- if$
- format.btitle "title" output.check
- crossref missing$
- { format.bvolume output
- format.number.series output
- publisher "publisher" output.check
- address output
- }
- { format.book.crossref output.nonnull }
- if$
- format.edition output
- format.date "year" output.check
- new.block
- note output
- fin.entry
-}
-
-FUNCTION {booklet}
-{ output.bibitem
- format.authors output
- format.title "title" output.check
- howpublished new.block.checka
- howpublished output
- address output
- format.date output
- new.block
- note output
- fin.entry
-}
-
-FUNCTION {inbook}
-{ output.bibitem
- author empty$
- { format.editors "author and editor" output.check }
- { format.authors output.nonnull
- crossref missing$
- { "author and editor" editor either.or.check }
- 'skip$
- if$
- }
- if$
- format.btitle "title" output.check
- crossref missing$
- { format.bvolume output
- format.number.series output
- publisher "publisher" output.check
- address output
- }
- { format.book.crossref output.nonnull }
- if$
- format.edition output
- format.date "year" output.check
- format.chapter.pages "chapter and pages" output.check
- new.block
- note output
- fin.entry
-}
-
-FUNCTION {incollection}
-{ output.bibitem
- format.authors "author" output.check
- format.title "title" output.check
- crossref missing$
- { format.in.ed.booktitle "booktitle" output.check
- format.bvolume output
- format.number.series output
- publisher "publisher" output.check
- address output
- format.edition output
- format.date "year" output.check
- }
- { format.incoll.inproc.crossref output.nonnull }
- if$
- format.chapter.pages output
- new.block
- note output
- fin.entry
-}
-
-FUNCTION {inproceedings}
-{ output.bibitem
- format.authors "author" output.check
- format.title "title" output.check
- crossref missing$
- { format.in.ed.booktitle "booktitle" output.check
- format.bvolume output
- format.number.series output
- address empty$
- { organization output
- publisher output
- format.date "year" output.check
- }
- { address output.nonnull
- format.date "year" output.check
- organization output
- publisher output
- }
- if$
- }
- { format.incoll.inproc.crossref output.nonnull }
- if$
- format.pages output
- new.block
- note output
- fin.entry
-}
-
-FUNCTION {conference} { inproceedings }
-
-FUNCTION {manual}
-{ output.bibitem
- author empty$
- { format.organization output }
- { format.authors output.nonnull }
- if$
- format.btitle "title" output.check
- author empty$
- 'skip$
- { organization output }
- if$
- address output
- format.edition output
- format.date output
- new.block
- note output
- fin.entry
-}
-
-FUNCTION {mastersthesis}
-{ output.bibitem
- format.authors "author" output.check
- format.title "title" output.check
- "Master's thesis" format.thesis.type output.nonnull
- school "school" output.check
- address output
- format.date "year" output.check
- new.block
- note output
- fin.entry
-}
-
-FUNCTION {misc}
-{ output.bibitem
- format.authors output
- format.title output
- howpublished new.block.checka
- howpublished output
- format.date output
- new.block
- note output
- fin.entry
- empty.misc.check
-}
-
-FUNCTION {phdthesis}
-{ output.bibitem
- format.authors "author" output.check
- format.btitle "title" output.check
- "PhD thesis" format.thesis.type output.nonnull
- school "school" output.check
- address output
- format.date "year" output.check
- new.block
- note output
- fin.entry
-}
-
-FUNCTION {proceedings}
-{ output.bibitem
- editor empty$
- { format.organization output }
- { format.editors output.nonnull }
- if$
- format.btitle "title" output.check
- format.bvolume output
- format.number.series output
- address empty$
- { editor empty$
- 'skip$
- { organization output }
- if$
- publisher output
- format.date "year" output.check
- }
- { address output.nonnull
- format.date "year" output.check
- editor empty$
- 'skip$
- { organization output }
- if$
- publisher output
- }
- if$
- new.block
- note output
- fin.entry
-}
-
-FUNCTION {techreport}
-{ output.bibitem
- format.authors "author" output.check
- format.title "title" output.check
- format.tr.number output.nonnull
- institution "institution" output.check
- address output
- format.date "year" output.check
- new.block
- note output
- fin.entry
-}
-
-FUNCTION {unpublished}
-{ output.bibitem
- format.authors "author" output.check
- format.title "title" output.check
- new.block
- note "note" output.check
- format.date output
- fin.entry
-}
-
-FUNCTION {default.type} { misc }
-
-MACRO {jan} {"Jan."}
-
-MACRO {feb} {"Feb."}
-
-MACRO {mar} {"Mar."}
-
-MACRO {apr} {"Apr."}
-
-MACRO {may} {"May"}
-
-MACRO {jun} {"June"}
-
-MACRO {jul} {"July"}
-
-MACRO {aug} {"Aug."}
-
-MACRO {sep} {"Sept."}
-
-MACRO {oct} {"Oct."}
-
-MACRO {nov} {"Nov."}
-
-MACRO {dec} {"Dec."}
-
-MACRO {acmcs} {"ACM Comput. Surveys"}
-
-MACRO {acta} {"Acta Inf."}
-
-MACRO {cacm} {"Comm. ACM"}
-
-MACRO {ibmjrd} {"IBM J. Res. Dev."}
-
-MACRO {ibmsj} {"IBM Syst.~J."}
-
-MACRO {ieeese} {"IEEE Trans. Softw. Eng."}
-
-MACRO {ieeetc} {"IEEE Trans. Comput."}
-
-MACRO {ieeetcad}
- {"IEEE Trans. Comput.-Aided Design Integrated Circuits"}
-
-MACRO {ipl} {"Inf. Process. Lett."}
-
-MACRO {jacm} {"J.~Assoc. Comput. Mach."}
-
-MACRO {jcss} {"J.~Comput. System Sci."}
-
-MACRO {scp} {"Sci. Comput. Programming"}
-
-MACRO {sicomp} {"SIAM J. Comput."}
-
-MACRO {tocs} {"ACM Trans. Comput. Syst."}
-
-MACRO {tods} {"ACM Trans. Database Syst."}
-
-MACRO {tog} {"ACM Trans. Gr."}
-
-MACRO {toms} {"ACM Trans. Math. Softw."}
-
-MACRO {toois} {"ACM Trans. Office Inf. Syst."}
-
-MACRO {toplas} {"ACM Trans. Prog. Lang. Syst."}
-
-MACRO {tcs} {"Theoretical Comput. Sci."}
-
-READ
-
-FUNCTION {sortify}
-{ purify$
- "l" change.case$
-}
-
-INTEGERS { len }
-
-FUNCTION {chop.word}
-{ 's :=
- 'len :=
- s #1 len substring$ =
- { s len #1 + global.max$ substring$ }
- 's
- if$
-}
-
-FUNCTION {sort.format.names}
-{ 's :=
- #1 'nameptr :=
- ""
- s num.names$ 'numnames :=
- numnames 'namesleft :=
- { namesleft #0 > }
- { nameptr #1 >
- { " " * }
- 'skip$
- if$
- s nameptr "{vv{ } }{ll{ }}{ f{ }}{ jj{ }}" format.name$ 't :=
- nameptr numnames = t "others" = and
- { "et al" * }
- { t sortify * }
- if$
- nameptr #1 + 'nameptr :=
- namesleft #1 - 'namesleft :=
- }
- while$
-}
-
-FUNCTION {sort.format.title}
-{ 't :=
- "A " #2
- "An " #3
- "The " #4 t chop.word
- chop.word
- chop.word
- sortify
- #1 global.max$ substring$
-}
-
-FUNCTION {author.sort}
-{ author empty$
- { key empty$
- { "to sort, need author or key in " cite$ * warning$
- ""
- }
- { key sortify }
- if$
- }
- { author sort.format.names }
- if$
-}
-
-FUNCTION {author.editor.sort}
-{ author empty$
- { editor empty$
- { key empty$
- { "to sort, need author, editor, or key in " cite$ * warning$
- ""
- }
- { key sortify }
- if$
- }
- { editor sort.format.names }
- if$
- }
- { author sort.format.names }
- if$
-}
-
-FUNCTION {author.organization.sort}
-{ author empty$
- { organization empty$
- { key empty$
- { "to sort, need author, organization, or key in " cite$ * warning$
- ""
- }
- { key sortify }
- if$
- }
- { "The " #4 organization chop.word sortify }
- if$
- }
- { author sort.format.names }
- if$
-}
-
-FUNCTION {editor.organization.sort}
-{ editor empty$
- { organization empty$
- { key empty$
- { "to sort, need editor, organization, or key in " cite$ * warning$
- ""
- }
- { key sortify }
- if$
- }
- { "The " #4 organization chop.word sortify }
- if$
- }
- { editor sort.format.names }
- if$
-}
-
-FUNCTION {presort}
-{ type$ "book" =
- type$ "inbook" =
- or
- 'author.editor.sort
- { type$ "proceedings" =
- 'editor.organization.sort
- { type$ "manual" =
- 'author.organization.sort
- 'author.sort
- if$
- }
- if$
- }
- if$
- " "
- *
- year field.or.null sortify
- *
- " "
- *
- title field.or.null
- sort.format.title
- *
- #1 entry.max$ substring$
- 'sort.key$ :=
-}
-
-ITERATE {presort}
-
-SORT
-
-STRINGS { longest.label }
-
-INTEGERS { number.label longest.label.width }
-
-FUNCTION {initialize.longest.label}
-{ "" 'longest.label :=
- #1 'number.label :=
- #0 'longest.label.width :=
-}
-
-FUNCTION {longest.label.pass}
-{ number.label int.to.str$ 'label :=
- number.label #1 + 'number.label :=
- label width$ longest.label.width >
- { label 'longest.label :=
- label width$ 'longest.label.width :=
- }
- 'skip$
- if$
-}
-
-EXECUTE {initialize.longest.label}
-
-ITERATE {longest.label.pass}
-
-FUNCTION {begin.bib}
-{ preamble$ empty$
- 'skip$
- { preamble$ write$ newline$ }
- if$
- "\begin{thebibliography}{" longest.label * "}" * write$ newline$
-}
-
-EXECUTE {begin.bib}
-
-EXECUTE {init.state.consts}
-
-EXECUTE {init.last.authors}
-
-ITERATE {call.type$}
-
-FUNCTION {end.bib}
-{ newline$
- "\end{thebibliography}" write$ newline$
-}
-
-EXECUTE {end.bib}
-
diff --git a/Master/texmf-dist/source/latex/siam/ptexconf.all b/Master/texmf-dist/source/latex/siam/ptexconf.all
deleted file mode 100644
index 06e2a7f38ae..00000000000
--- a/Master/texmf-dist/source/latex/siam/ptexconf.all
+++ /dev/null
@@ -1,102 +0,0 @@
-
-Please answer the following:
-
-1. Name of conference
-2. Type of Presentation
- Contributed: Lecture form or Poster form
- Minisymposium:
-
-3. Equipment for Visual Support
- Lecture form/Minisymposium: Overhead Projector or
- 2" x 2" Slide Projector (35mm)
-
- Poster form: Easel or Poster Board
-
-4. If you are a speaker in a minisymposium, who is the organizer?
-
-5. What is the minisymposium title?
-
-6. If more than one author, who will present the paper?
-
-
-%This is a macro file for creating a SIAM Conference abstract in
-% Plain Tex.
-%
-% If you have any questions regarding these macros contact:
-% Lillian Hunt
-% SIAM
-% 3600 University City Center Center
-% Philadelphia, PA 19104-2688
-% USA
-% (215) 382-9800
-% e-mail:meetings@siam.org
-
-
-\hsize=25.5pc
-\vsize=50pc
-\parskip=3pt
-\parindent=0pt
-\overfullrule=0pt
-\nopagenumbers
-
-\def\title#1\\{\bf{#1}\vskip6pt}
-\def\abstract#1\\{\rm {#1}}
-\def\author#1\\{\vskip6pt\rm {#1}\vfill\eject}
-\def\eol{\hfill\break}
-
-% end of style file
-
-% This is ptexconf.tex. Use this file as an example of a SIAM
-% Conference abstract in plain TeX.
-
-\input ptexconf.sty
-
-\title Numerical Analysis of a 1-Dimensional
-Immersed-Boundary Method\\
-
-\abstract We present the numerical analysis of a simplified,
-one-dimensional version
-of Peskin's immersed boundary method, which has been used to
-solve
-the two- and three-dimensional Navier-Stokes equations in the
-presence of immersed boundaries. We consider the heat
-equation
- in a finite domain with a moving source term.
-We denote the solution as $u(x,t)$ and the location of the
-source
- term as $X(t)$. The source term is a moving delta function
-whose strength is a function of u at the location of the
-delta function.
-The p.d.e. is coupled to an ordinary differential equation
-whose
-solution gives the location of the source term.
- The o.d.e. is $X'(t) = u(X(t),t)$, which can be interpreted as
-saying the source term moves at the local velocity.
-The accuracy the numerical method of solution depends on how
-the
-delta function is discretized when the delta function is not
-at
-a grid point and on how the solution, u, is represented
- at locations between grid points. We present results showing
-the effect of different choices of spreading the source to
-the grid and
-of restricting the solution to the source location.
-The problem we analyze is also similar to the Stefan problem
-and
-the immersed-boundary method has features in common with
-particle-in-cell
- methods.\\
- \author\underbar{Richard P. Beyer, Jr.}\eol
-University of Washington, Seattle, WA\eol
-%\vskip3pt
-Randall J. LeVeque\eol
-University of Washington, Seattle, WA\\
-\bye
-
-% end of example file
-
-
-Please furnish complete addresses for all co-authors.
-
-
-PLEASE BE SURE TO INDICATE WHAT CONFERENCE THE ABSTRACT IS FOR. \ No newline at end of file
diff --git a/Master/texmf-dist/source/latex/siam/ptexnec.all b/Master/texmf-dist/source/latex/siam/ptexnec.all
deleted file mode 100644
index 2da4cfce16f..00000000000
--- a/Master/texmf-dist/source/latex/siam/ptexnec.all
+++ /dev/null
@@ -1,707 +0,0 @@
-
-
-This file (ptexnec.all) constitutes the full distribution of NEC Proceedings Series
-Plain TeX macros. The files are:
-
-ptexnec.tex (An example file, also containing documentation)
-
-ptexnec.sty (the style file)
-
-To use these macros, separate at the indicated cut lines.
-
-%%%%%%%%%%%%%%%%%%%%%%%%%CUT HERE%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-% This is ptexnec.tex, an example file for use with the NEC Plain TeX
-% Proceedings Series macros. Comments are placed at the beginning and
-% throughout this file. Please take the time to read them as they document
-% how to use these macros. This file can be composed and printed out for
-% use as sample output. Please ignore the underfull \vbox on page 3.
-
-% Any comments or questions regarding these macros should be directed to:
-%
-% Corey Gray
-% SIAM
-% 3600 University City Science Center
-% Philadelphia, PA 19104-2688
-% USA
-% Telephone: (215) 382-9800
-% Fax: (215) 386-7999
-% e-mail: gray@siam.org
-
-
-% This file is to be used as an example for style only. It should not be read
-% for content.
-
-%%%%%%%%%%%%%%% PLEASE NOTE THE FOLLOWING STYLE RESTRICTIONS %%%%%%%%%%%%%%%
-
-%% 1. You must use the numbered reference style([1],[2]), listing the
-%% references at the end of the chapter either by order of citation
-%% or alphabetically.
-%%
-%% 2. This macro is set up for three levels of headings. Use the commands
-%% \headone, \headtwo, and \headthree. The macro will automatically
-%% number the headings.
-%%
-%% 3. The running heads are defined by the commands \def\leftrh{} and
-%% \def\rightrh{}. You must fill in the empty field of these commands
-%% with the appropriate information. The left running head should be the
-%% authors names. For papers with multiple authors, please follow these
-%% rules; for two authors type {Author 1 and Author 2}; for more than two
-%% authors type {Author 1 et al.}. The right running head is the title of
-%% the paper. If the title is more than 50 characters, including spaces,
-%% please provide a shortened version. All information should be typed
-%% initial cap and lower case.
-%%
-%% 5. Theorems, Lemmas, Definitions, etc. are to be double-numbered,
-%% indicating the section and the occurrence of that element
-%% within that section. (For example, the first theorem in the second
-%% section would be numbered 2.1.) This numbering must
-%% be done manually.
-%%
-%% 6. Proofs are handled by \prf\endprf. If you want to use an end-of-proof
-%% box, insert \qed right before the \endprf command.
-%%
-%% 7. Figures and equations must be manually single-numbered. Use \leqno
-%% for equation numbering. The macro provides the \fig for including
-%% figures. This command consists of three fields. The first field is
-%% used for inserting the appropriate space for the figure. The second
-%% field is the figure number. The third field is the caption. See the
-%% example included in this file. SIAM supports the use of psfig for
-%% including Postscript figures. All Postscript figures should be sent
-%% as separate files. A hardcopy version of all Postscript figures is
-%% also required. See note regarding this under How to Submit Your Paper.
-%%
-%% 8. Use of \title\endtitle and \lasttitle\endlastitle.
-%% This macro package provides two possible commands for handling the
-%% title of your paper. The commands \title\endtitle should be used for
-%% all lines except the last line of multiple line titles. The commands
-%% \lasttitle\endlasttitle should be used for the last line of multiple
-%% line titles. In the case of a single line title, \lasttitle\endlasttitle
-%% should be used.
-%%
-%% 9. Use of \author\endauthor and \lastauthor\endlastauthor.
-%% As in the title macro, two possible commands are provided for the
-%% author. The commands \author\endauthor should be used for the first
-%% line of authors if there are more than one line. The commands
-%% \lastauthor\endlastauthor should be used for the last line
-%% of multiple lines of authors. In the case of a single line of authors,
-%% \lastauthor\endlastauthor should be used. A maximum of four authors
-%% should be placed on any one line. The appropriate space must also be
-%% hard coded between authors on the same line. The spacing is as follows:
-%%
-%% If 2 authors; \hskip4pc between
-%% If 3 authors; \hskip3pc between
-%% If 4 authors; \hskip2pc between
-%%
-%% 10. Grant information and author affiliations.
-%% This information is included by using the \footnote command and the
-%% appropriate footnote symbol. SIAM uses footnote symbols in a
-%% particular order. Below is a list of these symbols:
-%%
-%% asterisk
-%% single-dagger
-%% double-dagger
-%% section sign
-%% paragraph
-%% parallel
-%% double asterisk
-%% double single-dagger
-%% double double-dagger
-%%
-%% For illustrative purposes, all footnote symbols have been used in the
-%% example file.
-%%
-%% A note regarding \footnote. This command seems to leave extra white
-%% space between footnotes. This is quite evident in the example file. If
-%% any user of these macros has a solution to this problem, I would
-%% appreciate hearing from you. Send your comments to: gray@siam.org.
-%%
-%% The following general rules apply for including grants and affiliations:
-%% a) If there is a single grant for the paper, then the grant
-%% information should be footnoted to the title.
-%% b) If there is more than one grant, included the grant information
-%% with each authors affiliation.
-%% c) If there are different grants for the paper but the authors share
-%% the same affiliation, footnote the grant information to the title.
-%% For example, The work of the first author was supported by xyz.
-%% The work of the second author was supported by abc. And so on.
-%%
-%%
-%% 11. Special fonts.
-%% SIAM supports the use of AMS-TeX fonts version 2.0 and later. As
-%% described in the manual for these fonts, they can be included by
-%% \input{amssym.def} and \input{amssym.tex}.
-%%
-%% 12. How to Submit Your Paper.
-%% The electronic version of your paper should be sent to proceed@siam.org.
-%% A hardcopy version should also be submitted. Instructions are included
-%% in your acceptance letter. Please be sure to send hardcopy
-%% versions of any Postscript figures you have submitted electronically.
-%% Be sure to return your signed Copyright Transfer Agreement. We cannot
-%% publish your paper without one.%%
-%%
-%%
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-\input ptexnec.sty
-
-\def\leftrh{Gray et al.}
-\def\rightrh{NEC Proceedings Series Macros}
-
-\startchapter %Place this command at the beginning of the file immediately
- %after the \input command.
-
-
-
-\title Chapter 1\endtitle
-\title NEC Proceedings Series Macros\endtitle
-\lasttitle for Use with Plain TeX\footnote*{Any information
-regarding grants should be placed here.}\endlasttitle
-
-\author J. Corey Gray\footnote{$^{\dag}$}{Production Manager, Society for
-Industrial and Applied Mathematics, Philadelphia, PA.}
-\hskip2truepc Tricia Manning\footnote{$^{\ddag}$}{Publications
-Specialist, Society for Industrial and Applied Mathematics, Philadelphia,
-PA.}
-\hskip2truepc Vickie Kearn\footnote{$^{\S}$}{Publisher, Society for Industrial
-and Applied Mathematics, Philadelphia, PA.}
-\hskip2truepc Nancy Abbott\footnote{$^{\P}$}{Design Supervisor, Society for
-Industrial and Applied Mathematics, Philadelphia, PA.}
-\endauthor
-\lastauthor Sue Ciambrano\footnote{$^{\parallel}$}{Acquisition Editor, Society for
-Industrial and Applied Mathematics, Philadelphia, PA.}
-\hskip2truepc Paul Duggan\footnote{$^{**}$}{Composition
-Specialist, Society for Industrial and Applied Mathematics, Philadelphia,
-PA.}
-\hskip2truepc Robbi Anne Albert\footnote{$^{\dagger\dagger}$}{Production,
-Assistant, Society for Industrial
-and Applied Mathematics, Philadelphia, PA.}
-\hskip2truepc Jean Anderson\footnote{$^{\ddag\ddag}$}{Composition Coordinator, Society for
-Industrial and Applied Mathematics, Philadelphia, PA.}
-\endlastauthor
-
-% Use \headone for the first level headings. The macro will automatically
-% number the headings.
-
-\centerline{\bf Abstract}
-\abstract An equivalence is shown between realizability of input/output (i/o) operators by
-rational control systems and high-order algebraic differential equations for
-i/o pairs. This generalizes, to nonlinear systems, the equivalence
-between autoregressive representations and finite dimensional linear
-realizability.\endabstract
-
-
-\headone{Problem Specification}
-In this paper, we consider the solution of the $N \times N$ linear
-system
-$$A x = b\leqno (1)$$
-where $A$ is large, sparse, symmetric, and positive definite. We consider
-the direct solution of by means of general sparse Gaussian
-elimination. In such a procedure, we find a permutation matrix $P$, and
-compute the decomposition
-$$
-P A P^{t} = L D L^{t}
-\leqno (2)$$
-
-\noindent where $L$ is unit lower triangular and $D$ is diagonal.
-
-
-\headone{Design Considerations}
-Several good ordering algorithms (nested dissection and minimum degree)
-are available for computing $P$ [1], [2].
-Since our interest here does not
-focus directly on the ordering, we assume for convenience that $P=I$,
-or that $A$ has been preordered to reflect an appropriate choice of $P$.
-
-% Use \thm and \endthm for theorems. They must be numbered manually.
-% Lemmas (\lem \endlem), corollaries (\cor \endcor), and
-% propositions (\prop \endprop) are coded the same as theorems and must
-% also be numbered manually.
-
-\thm{Theorem 2.1.} The method was extended to three
-dimensions. For the standard multigrid
-coarsening
-(in which, for a given grid, the next coarser grid has $1/8$
-as many points), anisotropic problems require plane
-relaxation to
-obtain a good smoothing factor.\endthm
-
-Several good ordering algorithms (nested dissection and minimum degree)
-are available for computing $P$ [1], [2].
-Since our interest here does not
-focus directly on the ordering, we assume for convenience that $P=I$,
-or that $A$ has been preordered to reflect an appropriate choice of $P$.
-Several good ordering algorithms (nested dissection and minimum degree)
-are available for computing $P$ [1], [2].
-Since our interest here does not
-focus directly on the ordering, we assume for convenience that $P=I$,
-or that $A$ has been preordered to reflect an appropriate choice of $P$.
-
-% Use \prf and \endprf to begin and end a proof.
-% The use of \qed will produce an end-of-proof box.
-
-\prf{Proof} In this paper we consider two methods. The first method
-is
-basically the method considered with two differences:
-first, we perform plane relaxation by a two-dimensional
-multigrid method, and second, we use a slightly different
-choice of
-interpolation operator, which improves performance
-for nearly singular problems. In the second method coarsening
-is done by successively coarsening each.\qed\endprf
-
-% Use \dfn and \enddfn to begin and end definitions.
-
-\dfn{Definition 2.1.}We describe the two methods in \S\ 1.2. This is a
-definition in the plain tex macro.\enddfn
-
-This is accomplished by exploiting the m-tree,
-a particular spanning tree for the graph of the filled-in matrix.
-Our purpose here is to examine the nonnumerical complexity of the
-sparse elimination algorithm given in [3].
-As was shown there, a general sparse elimination scheme based on the
-bordering algorithm requires less storage for pointers and
-row/column indices than more traditional implementations of general
-sparse elimination. This is accomplished by exploiting the m-tree,
-a particular spanning tree for the graph of the filled-in matrix.
-
-
-Our purpose here is to examine the nonnumerical complexity of the
-sparse elimination algorithm given in [3].
-As was shown there, a general sparse elimination scheme based on the
-bordering algorithm requires less storage for pointers and
-row/column indices than more traditional implementations of general
-sparse elimination. This is accomplished by exploiting the m-tree,
-a particular spanning tree for the graph of the filled-in matrix.
-Since our interest here does not
-focus directly on the ordering, we assume for convenience that $P=I$,
-or that $A$ has been preordered to reflect an appropriate choice of $P$.
-
-% Use \lem and \endlem to begin and end lemmas.
-
-\lem{Lemma 2.1.}We discuss first the choice for $I_{k-1}^k$
-which is a generalization. We assume that $G^{k-1}$ is
-obtained
-from $G^k$
-by standard coarsening; that is, if $G^k$ is a tensor product
-grid $G_{x}^k \times G_{y}^k \times G_{z}^k$,
-$G^{k-1}=G_{x}^{k-1} \times G_{y}^{k-1} \times G_{z}^{k-1}$,
-where $G_{x}^{k-1}$ is obtained by deleting every other grid
-point of $G_x^k$ and similarly for $G_{y}^k$ and $G_{z}^k$.
-\endlem
-
-% Use \fig to insert space for figures .
-
-\fig{10pc}{Fig. 1}{This is the caption for figure one.}
-
-To our knowledge, the m-tree previously has not been applied in this
-fashion to the numerical factorization, but it has been used,
-directly or indirectly, in several optimal order algorithms for
-computing the fill-in during the symbolic factorization phase
-[4] - [10], [5], [6]. In \S 1.3., we analyze the complexity of the old and new
-approaches to the intersection problem for the special case of
-an $n \times n$ grid ordered by nested dissection. The special
-structure of this problem allows us to make exact estimates of
-the complexity. To our knowledge, the m-tree previously has not been applied in this
-fashion to the numerical factorization, but it has been used,
-directly or indirectly, in several optimal order algorithms for
-computing the fill-in during the symbolic factorization phase
-[4] - [10], [5], [6].
-
-% Use \headtwo for second level headings. They will be numbered automatically.
-
-\headtwo{Robustness}In \S 1.2, we review the bordering algorithm, and introduce
-the sorting and intersection problems that arise in the
-sparse formulation of the algorithm.
-
-\headtwo{Versatility} In \S 1.3., we analyze the complexity of the old and new
-approaches to the intersection problem for the special case of
-an $n \times n$ grid ordered by nested dissection. The special
-structure of this problem allows us to make exact estimates of
-the complexity. To our knowledge, the m-tree previously has not been applied in this
-fashion to the numerical factorization, but it has been used,
-directly or indirectly, in several optimal order algorithms for
-computing the fill-in during the symbolic factorization phase
-[4] - [10], [5], [6].
-
-
-% Use \headthree for third level headings.
-
-\headthree{Complexity.}For the old approach, we show that the
-complexity of the intersection problem is $O(n^{3})$, the same
-as the complexity of the numerical computations. For the
-new approach, the complexity of the second part is reduced to
-$O(n^{2} (\log n)^{2})$.
-
-% The command \Refs sets the word Reference as a heading and allows the proper
-% amount of space before the start of the references. Each reference must
-% begin with \ref\\. The article or title of the reference should be in
-% italic. Use the \it command within brackets. End each reference with
-% \endref and allow two returns between references. Use the command
-% \sameauthor (see reference 8) when the same author or group of authors
-% is listed consecutively.
-
-\Refs
-
-\ref 1\\R.~E. Bank, {\it PLTMG users' guide, edition 5.0}, tech. report,
- Department of Mathematics, University of California, San Diego, CA, 1988.\endref
-
-\ref 2\\R.~E. Bank, T.~F. Dupont, and H.~Yserentant, {\it The hierarchical basis
- multigrid method}, Numer. Math., 52 (1988), pp.~427--458.\endref
-
-\ref 3\\R.~E. Bank and R.~K. Smith, {\it General sparse elimination requires no
- permanent integer storage}, SIAM J. Sci. Stat. Comput., 8 (1987),
- pp.~574--584.\endref
-
-\ref 4\\S.~C. Eisenstat, M.~C. Gursky, M.~Schultz, and A.~Sherman, {\it
- Algorithms and data structures for sparse symmetric gaussian elimination},
- SIAM J. Sci. Stat. Comput., 2 (1982), pp.~225--237.\endref
-
-\ref 5\\A.~George and J.~Liu, {\it Computer Solution of Large Sparse Positive
- Definite Systems}, Prentice Hall, Englewood Cliffs, NJ, 1981.\endref
-
-\ref 6\\K.~H. Law and S.~J. Fenves, {\it A node addition model for symbolic
- factorization}, ACM TOMS, 12 (1986), pp.~37--50.\endref
-
-\ref 7\\J.~W.~H. Liu, {\it A compact row storage scheme for cholesky factors
- using elimination trees}, ACM TOMS, 12 (1986), pp.~127--148.\endref
-
-\ref 8\\\sameauthor , {\it The role of
- elimination trees in sparse factorization}, Tech. Report CS-87-12,Department
- of Computer Science, York University, Ontario, Canada, 1987.\endref
-
-\ref 9\\D.~J. Rose, {\it A graph theoretic study of the numeric solution of
- sparse positive definite systems}, in Graph Theory and Computing,
- Academic Press, New York, 1972.\endref
-
-\ref 10\\D.~J. Rose, R.~E. Tarjan, and G.~S. Lueker, {\it Algorithmic aspects of
- vertex elimination on graphs}, SIAM J. Comput., 5 (1976), pp.~226--283.\endref
-
-\vfill\eject
-
-Extra page.
-\vfill
-\bye
-%%% End of example file
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%CUT HERE%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-% This file may be freely distributed but may not be altered in any way.
-% Any comments or questions regarding these macros should be directed to:
-
-% Corey Gray
-% SIAM
-% 3600 University City Science Center
-% Philadelphia, PA 19104-2688
-% USA
-% Telephone: (215) 382-9800
-% Fax: (215) 386-7999
-% e-mail: gray@siam.org
-
-%
-% This is a file of macros and definitions for creating a chapter
-% for publication in the NEC Proceedings Series using Plain TeX.
-
-% Report the version.
-\message{*** NEC Plain TeX Proceedings Series macro package, version 1.0,
-November 6, 1992.***}
-
-% Make the @ sign a letter for internal control sequences.
-\catcode`\@=11
-%
-%
-%
-
-
-\baselineskip=14truept
-
-
-%%% DIMENSIONS %%%
-
-\hsize=30truepc
-\vsize=49truepc
-%\hoffset=.5in
-\parindent=18truept
-\def\firstpar{\parindent=0pt\global\everypar{\parindent=18truept}}
-\parskip=0pt
-
-
-%%% FONTS %%%
-
-\font\tenrm=cmr10
-\font\tenbf=cmbx10
-\font\tenit=cmti10
-\font\tensmc=cmcsc10
-\def\tenpoint{%
- \def\rm{\tenrm}\def\bf{\tenbf}%
- \def\it{\tenit}\def\smc{\tensmc}
- \textfont0=\tenrm \scriptfont0=\sevenrm
- \textfont1=\teni \scriptfont1=\seveni
- \textfont2=\tensy \scriptfont2=\sevensy
- \textfont3=\tenex \scriptfont3=\tenex
-\baselineskip=12pt\rm}%
-
-\font\ninerm=cmr9
-\font\ninebf=cmbx9
-\font\nineit=cmti9
-\def\ninepoint{%
- \def\rm{\ninerm}\def\bf{\ninebf}%
- \def\it{\nineit}\baselineskip=11pt\rm}%
-
-\font\eightrm=cmr8
-\font\eightbf=cmbx8
-\font\eightit=cmti8
-\font\eighti=cmmi8
-\font\eightsy=cmsy8
-\def\eightpoint{%
- \def\rm{\eightrm}\def\bf{\eightbf}%
- \def\it{\eightit}\def\smc{\eightrm}\baselineskip=10pt\rm%
- \textfont0=\eightrm \scriptfont0=\sixrm
- \textfont1=\eighti \scriptfont1=\sixi
- \textfont2=\eightsy \scriptfont2=\sixsy
- \textfont3=\tenex \scriptfont3=\tenex
-}
-
-\font\sixrm=cmr6
-\font\sixbf=cmbx6
-\font\sixi=cmmi6
-\font\sixsmc=cmr5
-\font\sixsy=cmsy6
-\def\sixpoint{%
- \def\rm{\sixrm}\def\bf{\sixbf}%
- \def\smc{\sixsmc}\baselineskip=8pt\rm}%
-
-\fontdimen13\tensy=2.6pt
-\fontdimen14\tensy=2.6pt
-\fontdimen15\tensy=2.6pt
-\fontdimen16\tensy=1.2pt
-\fontdimen17\tensy=1.2pt
-\fontdimen18\tensy=1.2pt
-
-\font\eightrm=cmr8
-\font\ninerm=cmr9
-\font\elevenrm=cmr10 scaled\magstephalf
-\font\fourteenrm=cmr10 scaled\magstep 1
-\font\eighteenrm=cmr10 scaled\magstep 3
-\font\twelvebf=cmbx10 scaled\magstep 1
-\font\elevenbf=cmbx10 scaled\magstephalf
-\font\elevenit=cmti10 scaled\magstephalf
-\font\elevensc=cmcsc10 scaled\magstephalf
-
-\def\theoremfont{\elevensc}
-\def\textfont{\elevenrm}
-\def\itfont{\elevenit}
-\def\headfont{\twelvebf}
-\def\smallheadfont{\elevenbf}
-\def\titlefont{\eighteenrm}
-\def\chapterfont{\fourteenrm}
-\def\authorfont{\fourteenrm}
-\def\rheadfont{\tenrm}
-\def\abstractfont{\tenrm}
-\def\smc{\tensmc}
-\font\eightsmc=cmcsc8
-
-\def\footnote#1{\baselineskip=11truept\edef\@sf{\spacefactor\the\spacefactor}#1\@sf
- \insert\footins\bgroup\ninepoint\hsize=36pc
- \interlinepenalty10000 \let\par=\endgraf
- \leftskip=0pt \rightskip=0pt
- \splittopskip=10pt plus 1pt minus 1pt \floatingpenalty=20000
-\smallskip
-\item{#1}\bgroup\baselineskip=10pt\strut
-\aftergroup\@foot\let\next}
-\skip\footins=12pt plus 2pt minus 4pt
-\dimen\footins=36pc
-
-
-
-%%% CHAPTER OPENING MACROS %%%
-
-\def\startchapter{\topinsert\vglue54pt\endinsert}
-
-\def\title#1\endtitle{\titlefont\centerline{#1}\vglue5pt}%\vskip40truept\tenrm}
-\def\lasttitle#1\endlasttitle{\titlefont\centerline{#1}\vskip1.32truepc}
-\def\author#1\endauthor{\authorfont\centerline{#1}\vglue8pt\textfont}
-\def\lastauthor#1\endlastauthor{\authorfont\centerline{#1}\vglue2.56pc\textfont}
-\def\abstract#1\endabstract{\baselineskip=12pt\leftskip=2.25pc
- \rightskip=2.25pc\abstractfont{#1}\textfont}
-
-%%% COUNTERS FOR HEADINGS %%%
-
-\newcount\headcount
-\headcount=1
-\newcount\seccount
-\seccount=1
-\newcount\subseccount
-\subseccount=1
-\def\secreset{\global\seccount=1}
- \def\subsecreset{\global\subseccount=1}
-
-%%% HEADINGS %%%
-
-\def\headone#1{\baselineskip=14pt\leftskip=0pt\rightskip=0pt\vskip17truept\parindent=0pt
-{\headfont\the\headcount\hskip14truept #1}
-\par\nobreak\firstpar\global\advance\headcount by 0
- \global\advance\headcount by 1\secreset\vskip2truept\textfont}
-
-\def\headtwo#1{\advance\headcount by -1%
- \vskip17truept\parindent=0pt{\headfont\the\headcount.%
- \the\seccount\hskip14truept #1}%\enspace\ignorespaces\firstpar
- \global\advance\headcount by 1\global\advance\seccount by 1
- \global\advance\subseccount by 1\subsecreset\vskip2pt\textfont}
-
- \def\headthree#1{\advance\headcount by -1\advance\seccount by -1
-% \advance\subseccount by -1%
- \vskip17truept\parindent=0pt{\smallheadfont\the\headcount.%
- \the\seccount.\the\subseccount\hskip11truept #1}\hskip6pt\ignorespaces
- \firstpar\global\advance\headcount by 1\global\advance\seccount by 1
- \global\advance\subseccount by 1\textfont}
-
-%%% THEOREMS, PROOFS, DEFINITIONS, etc. %%%
-
-\def\thm#1{{\theoremfont
-#1\enspace}
-\hskip-5pt\begingroup\itfont\ignorespaces}
-
-\let\lem=\thm
-\let\cor=\thm
-\let\prop=\thm
-
-\def\endthm{\endgroup\textfont}
-\let\endlem=\endthm
-\let\endcor=\endthm
-\let\endprop=\endthm
-
-\def\prf#1{{\itfont #1.}\textfont\enspace\ignorespaces}
-\let\rem=\prf
-\let\case=\prf
-
-\def\endprf{\textfont}
-\let\endrem=\endprf
-\let\endcase=\endprf
-
-\def\qed{{\qquad \vbox{\hrule\hbox{%
- \vrule height1.3ex\hskip0.8ex\vrule}\hrule
- }}\par}
-
-\def\dfn#1{{\theoremfont
-#1\enspace}
-\textfont\ignorespaces}
-
-\let\fact=\dfn
-
-\def\enddfn{\textfont}
-
-\let\endfact=\enddfn
-
-%%% FIGURES AND CAPTIONS %%%
-
-
-\newcount\figcount
-\figcount=1
-
-
-%\newcount\tablenumber
-%\tablenumber=1
-
-\def\\{\hfill\break}
-
-\newbox\TestBox
-\newdimen\setwd
-\newskip\belowcaptionskip
-\belowcaptionskip=6pt plus 1pt
-
-\def\endinsert{\egroup % finish the \vbox
- \if@mid \dimen@\ht\z@ \advance\dimen@\dp\z@
- \advance\dimen@12\p@ \advance\dimen@\pagetotal
- \ifdim\dimen@>\pagegoal\@midfalse\p@gefalse\fi\fi
- \if@mid\vskip\belowcaptionskip\box\z@\par \penalty-200\vskip\belowcaptionskip
- \else\insert\topins{\penalty100 % floating insertion
- \splittopskip\z@skip
- \splitmaxdepth\maxdimen \floatingpenalty\z@
- \ifp@ge \dimen@\dp\z@
- \vbox to\vsize{\unvbox\z@\kern-\dimen@}% depth is zero
- \else \box\z@\nobreak\vskip\belowcaptionskip\fi}\fi\endgroup}
-
-
-
-
-\def\fig#1#2#3{%
- \setbox\TestBox=\hbox{\tenpoint #3.}\setwd=\wd\TestBox
- \topinsert
- \vskip #1
- \vskip 12pt
- \ifdim\setwd > 23pc
- {\tenit{\smc #2.}\ \ #3}
- \else
- \centerline{\tenit\noindent
- {\smc #2.}\ \ #3}\fi%
- % \global\advance\figcount by 1
- \endinsert}
-
-
-
-%%% REFERENCES %%%
-
-\newdimen\refindent@
-\newdimen\refhangindent@
-\newbox\refbox@
-\setbox\refbox@=\hbox{\tenrm\baselineskip=11pt [00]}% Default 2 digits
-\refindent@=\wd\refbox@
-
-\def\resetrefindent#1{%
- \setbox\refbox@=\hbox{\tenrm\baselineskip=11pt [#1]}%
- \refindent@=\wd\refbox@}
-
-\def\Refs{%
- \unskip\vskip1pc
- \leftline{\noindent\headfont References}%
- \penalty10000
- \vskip4pt
- \penalty10000
- \refhangindent@=\refindent@
- \global\advance\refhangindent@ by .5em
- \global\everypar{\hangindent\refhangindent@}%
- \parindent=0pt\baselineskip=12pt\tenrm}
-
-\def\sameauthor{\leavevmode\vbox to 1ex{\vskip 0pt plus 100pt
- \hbox to 2em{\leaders\hrule\hfil}\vskip 0pt plus 300pt}}
-
-\def\ref#1\\#2\endref{\leavevmode\hbox to \refindent@{\hfil[#1]}\enspace #2\par}
-
-
-%%% OUTPUT %%%
-
-\def\rightheadline{\hfill\tenrm\rightrh\hskip2pc\tenrm\folio}
-\def\leftheadline{\tenrm\folio\hskip2pc\tenrm\leftrh\hfill}
-
-\global\footline={\hss\tenrm\folio\hss}% first page
-
-\output{\plainoutput}
-\def\plainoutput{\shipout\vbox{\makeheadline\pagebody\makefootline}%
- \advancepageno
- \ifnum\pageno>1
- \global\footline={\hfill}%
- \fi
- \ifodd\pageno
- \global\headline={\rightheadline}%
- \else
- \global\headline={\leftheadline}%
- \fi
- \ifnum\outputpenalty>-\@MM \else\dosupereject\fi}
-\def\pagebody{\vbox to\vsize{\boxmaxdepth\maxdepth \pagecontents}}
-\def\makeheadline{\vbox to\z@{\vskip-22.5\p@
- \line{\vbox to8.5\p@{}\rheadfont\the\headline}\vss}%
- \nointerlineskip}
-\def\makefootline{\baselineskip24\p@\vskip-6\p@\line{\the\footline}}
-\def\dosupereject{\ifnum\insertpenalties>\z@ % something is being held over
- \line{}\kern-\topskip\nobreak\vfill\supereject\fi}
-
-\def\footnoterule{\vskip11pt\kern -4\p@\hrule width 3pc \kern 3.6\p@ } % rule = .4 pt high
-
-% Turn off @ as being a letter.
-%
-\catcode`\@=13
-
-%end of style file
-
diff --git a/Master/texmf-dist/source/latex/siam/ptexpprt.all b/Master/texmf-dist/source/latex/siam/ptexpprt.all
deleted file mode 100644
index fb644d0fdf3..00000000000
--- a/Master/texmf-dist/source/latex/siam/ptexpprt.all
+++ /dev/null
@@ -1,724 +0,0 @@
-%% This is ptexpprt.all. This file is to be used for creating a paper
-%% in the ACM/SIAM Preprint series with Plain TeX. It consists of the following
-%% two files:
-%%
-%% ptexpprt.tex ---- an example and documentation file
-%% ptexpprt.sty ---- the macro file
-%%
-%% To use, cut this file apart at the appropriate places. You can run the
-%% example file with the macros to get sample output.
-%%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%% CUT HERE %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%
-%
-%%%%%%%%%%%%%%%%%%%%%%%%%% ptexpprt.tex %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%
-% This is ptexpprt.tex, an example file for use with the ACM/SIAM Plain TeX
-% Preprint Series macros. It is designed to produce double-column output.
-% Comments are placed at the beginning and throughout this file. Please
-% take the time to read them as they document how to use these macros.
-% This file can be composed and printed out for use as sample output.
-
-% Any comments or questions regarding these macros should be directed to:
-%
-% Corey Gray
-% SIAM
-% 3600 University City Science Center
-% Philadelphia, PA 19104-2688
-% USA
-% Telephone: (215) 382-9800
-% Fax: (215) 386-7999
-% e-mail: siampubs@wharton.upenn.edu
-
-
-% This file is to be used as an example for style only. It should not be read
-% for content.
-
-%%%%%%%%%%%%%%% PLEASE NOTE THE FOLLOWING STYLE RESTRICTIONS %%%%%%%%%%%%%%%
-
-%% 1. You must use the numbered reference style([1],[2]), listing the
-%% references at the end of the chapter either by order of citation
-%% or alphabetically.
-%%
-%% 2. Unless otherwise stated by your editor, do your chapter as if it
-%% is Chapter 1.
-%% If you know which number your chapter is, you must do the following:
-%%
-%% Go into the style file (ptexfrnt.sty) and search for the
-%% \def\chapter#1 definition. At the end of this definition
-%% there is a command \headcount=1. Change the 1 to
-%% the appropriate number. This change will cause the headings
-%% in your chapter to match the chapter number.
-%%
-%% 3. This macro is set up for two levels of headings. The macro will
-%% automatically number the headings for you.
-%%
-%% 4. The running heads are defined in the output routine. It will be
-%% necessary for you to alter the information currently included.
-%% To do this, go into the style file and search for OUTPUT. Once there,
-%% scroll through the file until you see the command \def\rhead. Replace
-%% CHAPTER TITLE with the title (or shortened title) of your paper.
-%% Replace AUTHORS NAMES with the appropriate names.
-%% Neither running head may be longer than 50 characters.
-%%
-%% 5. Theorems, Lemmas, Definitions, etc. are to be triple numbered,
-%% indicating the chapter, section, and the occurence of that element
-%% within that section. (For example, the first theorem in the second
-%% section of chapter three would be numbered 3.2.1. This numbering must
-%% be done manually.
-%%
-%% 6. Figures and equations must be manually double-numbered, indicating
-%% chapter and occurence. Use \leqno for equation numbering. See the
-%% example of \caption for figure numbering.
-%% Note. Although not shown, tables must also be double-numbered. The
-%% command \caption can also be used for table captions.
-%%
-%% 7. At the first occurence of each new element there is a description
-%% of how to use the coding.
-%%
-%%%%%%% PLEASE NOTE THE FOLLOWING POTENTIAL PROBLEMS:
-%
-%% 1. A bug exists that prevents a page number from printing on the first
-%% page of the paper. Please ignore this problem. It will be handled
-%% after you submit your paper.
-%%
-%% 2. The use of \topinsert and \midinsert to allow space for figures can
-%% result in unusual page breaks, or unusual looking pages in general.
-%% If you encounter such a situation, contact the SIAM office at the
-%% address listed above for instructions.
-%%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-\input ptexpprt.sty
-\voffset=.25in
-\titlepage
-
-% It will be necessary to hard code the chapter title and chapter authors.
-% You must decide where to break the lines. For the authors, please follow
-% the following conventions:
-% 1. If 2 authors are on a line, use \hskip4pc between them. If 3 authors,
-% use \hskip2pc. Do not put more than 3 authors on the same line.
-% 2. Use the following notation: asterisk, dagger, double-dagger, section
-% symbol, paragraph symbol, double asterisk. If more are needed, contact
-% the SIAM office.
-
-\centerline{\chapterfont Chapter 1}
-\vskip2pt
-\centerline{\titlefont SIAM/ACM Preprint Series Macros for
-Plain TeX\footnote*{Supported by GSF grants ABC123, DEF456, and GHI 789.}}
-\vskip15pt
-\centerline{\authorfont J. Corey Gray\footnote\dag{Society for Industrial and
-Applied Mathematics.}\hskip2pc Tricia Manning\footnote\ddag{Society for
-Industrial and Applied Mathematics.}\hskip2pc Vickie Kearn\footnote\S{Society
-for Industrial and Applied Mathematics.}}
-\vskip2pc
-
-\begindoublecolumns
-
-% Use \headone for the first level headings. The macro will automatically
-% number the headings.
-
-\headone{Problem Specification}
-In this paper, we consider the solution of the $N \times N$ linear
-system
-$$A x = b\leqno(1.1)$$
-where $A$ is large, sparse, symmetric, and positive definite. We consider
-the direct solution of by means of general sparse Gaussian
-elimination. In such a procedure, we find a permutation matrix $P$, and
-compute the decomposition
-$$
-P A P^{t} = L D L^{t}
-$$
-where $L$ is unit lower triangular and $D$ is diagonal.
-
-\headone{Design Considerations}
-Several good ordering algorithms (nested dissection and minimum degree)
-are available for computing $P$ [1], [2].
-Since our interest here does not
-focus directly on the ordering, we assume for convenience that $P=I$,
-or that $A$ has been preordered to reflect an appropriate choice of $P$.
-
-% Use \headtwo for second level headings. They will be numbered automatically.
-
-\headtwo{Robustness}In \S 1.2, we review the bordering algorithm, and introduce
-the sorting and intersection problems that arise in the
-sparse formulation of the algorithm.
-
-\headtwo{Versatility} In \S 1.3., we analyze the complexity of the old and new
-approaches to the intersection problem for the special case of
-an $n \times n$ grid ordered by nested dissection. The special
-structure of this problem allows us to make exact estimates of
-the complexity. To our knowledge, the m-tree previously has not been applied in
-this
-fashion to the numerical factorization, but it has been used,
-directly or indirectly, in several optimal order algorithms for
-computing the fill-in during the symbolic factorization phase
-[4] - [10], [5], [6].
-This is accomplished by exploiting the m-tree,
-a particular spanning tree for the graph of the filled-in matrix.
-Our purpose here is to examine the nonnumerical complexity of the
-sparse elimination algorithm given in [3].
-As was shown there, a general sparse elimination scheme based on the
-bordering algorithm requires less storage for pointers and
-row/column indices than more traditional implementations of general
-sparse elimination. This is accomplished by exploiting the m-tree,
-a particular spanning tree for the graph of the filled-in matrix.
-
-
-% Use \thm and \endthm for theorems. They must be numbered manually.
-% Lemmas (\lem \endlem), corollaries (\cor \endcor), and
-% propositions (\prop \endprop) are coded the same as theorems and must
-% also be numbered manually.
-
-\thm{Theorem 2.1.} The method was extended to three
-dimensions. For the standard multigrid
-coarsening
-(in which, for a given grid, the next coarser grid has $1/8$
-as many points), anisotropic problems require plane
-relaxation to
-obtain a good smoothing factor.\endthm
-
-Several good ordering algorithms (nested dissection and minimum degree)
-are available for computing $P$ [1], [2].
-Since our interest here does not
-focus directly on the ordering, we assume for convenience that $P=I$,
-or that $A$ has been preordered to reflect an appropriate choice of $P$.
-Several good ordering algorithms (nested dissection and minimum degree)
-are available for computing $P$ [1], [2].
-Since our interest here does not
-focus directly on the ordering, we assume for convenience that $P=I$,
-or that $A$ has been preordered to reflect an appropriate choice of $P$.
-
-% Use \prf to begin a proof.
-
-\prf{Proof} In this paper we consider two methods. The first method
-is
-basically the method considered with two differences:
-first, we perform plane relaxation by a two-dimensional
-multigrid method, and second, we use a slightly different
-choice of
-interpolation operator, which improves performance
-for nearly singular problems. In the second method coarsening
-is done by successively coarsening each.
-
-% Use \dfn to begin definitions.
-
-\dfn{Definition 1.2.1.}We describe the two methods in \S\ 1.2. This is a
-definition in the plain tex macro.
-
-This is accomplished by exploiting the m-tree,
-a particular spanning tree for the graph of the filled-in matrix.
-Our purpose here is to examine the nonnumerical complexity of the
-sparse elimination algorithm given in [3].
-As was shown there, a general sparse elimination scheme based on the
-bordering algorithm requires less storage for pointers and
-row/column indices than more traditional implementations of general
-sparse elimination. This is accomplished by exploiting the m-tree,
-a particular spanning tree for the graph of the filled-in matrix.
-Our purpose here is to examine the nonnumerical complexity of the
-sparse elimination algorithm given in [3].
-As was shown there, a general sparse elimination scheme based on the
-bordering algorithm requires less storage for pointers and
-row/column indices than more traditional implementations of general
-sparse elimination. This is accomplished by exploiting the m-tree,
-a particular spanning tree for the graph of the filled-in matrix.
-Since our interest here does not
-focus directly on the ordering, we assume for convenience that $P=I$,
-or that $A$ has been preordered to reflect an appropriate choice of $P$.
-
-
-To our knowledge, the m-tree previously has not been applied in this
-fashion to the numerical factorization, but it has been used,
-directly or indirectly, in several optimal order algorithms for
-computing the fill-in during the symbolic factorization phase
-[4] - [10], [5], [6]. In \S 1.3., we analyze the complexity of the old and new
-approaches to the intersection problem for the special case of
-an $n \times n$ grid ordered by nested dissection. The special
-structure of this problem allows us to make exact estimates of
-the complexity. To our knowledge, the m-tree previously has not been applied in
-this
-fashion to the numerical factorization, but it has been used,
-directly or indirectly, in several optimal order algorithms for
-computing the fill-in during the symbolic factorization phase
-[4] - [10], [5], [6].
-Several good ordering algorithms (nested dissection and minimum degree)
-are available for computing $P$ [1], [2].
-Since our interest here does not
-focus directly on the ordering, we assume for convenience that $P=I$,
-or that $A$ has been preordered to reflect an appropriate choice of $P$.
-For the old approach, we show that the
-complexity of the intersection problem is $O(n^{3})$, the same
-as the complexity of the numerical computations. For the
-new approach, the complexity of the second part is reduced to
-$O(n^{2} (\log n)^{2})$.
-
-% Use \midinsert along with \caption to allow space for
-% figures. See note above in problem section.
-%\midinsert\vskip15.5pc\caption{Fig. 1.1. {\nineit This is figure 1.}}
-% \endcaption\endinsert
-
-In this paper, we consider the solution of the $N \times N$ linear
-system
-where $A$ is large, sparse, symmetric, and positive definite. We consider
-the direct solution of by means of general sparse Gaussian
-elimination. In such a procedure, we find a permutation matrix $P$, and
-compute the decomposition
-where $L$ is unit lower triangular and $D$ is diagonal.
-
-\headone{Design Considerations}
-Several good ordering algorithms (nested dissection and minimum degree)
-are available for computing $P$ [1], [2].
-Since our interest here does not
-focus directly on the ordering, we assume for convenience that $P=I$,
-or that $A$ has been preordered to reflect an appropriate choice of $P$.
-
-Several good ordering algorithms (nested dissection and minimum degree)
-are available for computing $P$ [1], [2].
-Since our interest here does not
-focus directly on the ordering, we assume for convenience that $P=I$,
-or that $A$ has been preordered to reflect an appropriate choice of $P$.
-Several good ordering algorithms (nested dissection and minimum degree)
-are available for computing $P$ [1], [2].
-Since our interest here does not
-focus directly on the ordering, we assume for convenience that $P=I$,
-or that $A$ has been preordered to reflect an appropriate choice of $P$.
-Our purpose here is to examine the nonnumerical complexity of the
-sparse elimination algorithm given in [3].
-As was shown there, a general sparse elimination scheme based on the
-bordering algorithm requires less storage for pointers and
-row/column indices than more traditional implementations of general
-sparse elimination. This is accomplished by exploiting the m-tree,
-a particular spanning tree for the graph of the filled-in matrix.
-Since our interest here does not
-focus directly on the ordering, we assume for convenience that $P=I$,
-or that $A$ has been preordered to reflect an appropriate choice of $P$.
-
-% Use \lem and \endlem to begin and end lemmas.
-
-\lem{Lemma 2.1.}We discuss first the choice for $I_{k-1}^k$
-which is a generalization. We assume that $G^{k-1}$ is
-obtained
-from $G^k$
-by standard coarsening; that is, if $G^k$ is a tensor product
-grid $G_{x}^k \times G_{y}^k \times G_{z}^k$,
-$G^{k-1}=G_{x}^{k-1} \times G_{y}^{k-1} \times G_{z}^{k-1}$,
-where $G_{x}^{k-1}$ is obtained by deleting every other grid
-point of $G_x^k$ and similarly for $G_{y}^k$ and $G_{z}^k$.
-\endlem
-
-To our knowledge, the m-tree previously has not been applied in this
-fashion to the numerical factorization, but it has been used,
-directly or indirectly, in several optimal order algorithms for
-computing the fill-in during the symbolic factorization phase
-[4] - [10], [5], [6]. In \S 1.3., we analyze the complexity of the old and new
-approaches to the intersection problem for the special case of
-an $n \times n$ grid ordered by nested dissection. The special
-structure of this problem allows us to make exact estimates of
-the complexity. To our knowledge, the m-tree previously has not been applied in
-this
-fashion to the numerical factorization, but it has been used,
-directly or indirectly, in several optimal order algorithms for
-computing the fill-in during the symbolic factorization phase
-[4] - [10], [5], [6].
-
-% Use \headtwo for second level headings. They will be numbered automatically.
-
-\headone{Problem Solving}In \S 1.2, we review the bordering algorithm, and
-introduce
-the sorting and intersection problems that arise in the
-sparse formulation of the algorithm.
-
-\headtwo{Versatility} In \S 1.3., we analyze the complexity of the old and new
-approaches to the intersection problem for the special case of
-an $n \times n$ grid ordered by nested dissection. The special
-structure of this problem allows us to make exact estimates of
-the complexity. To our knowledge, the m-tree previously has not been applied in
-this
-fashion to the numerical factorization, but it has been used,
-directly or indirectly, in several optimal order algorithms for
-computing the fill-in during the symbolic factorization phase
-[4] - [10], [5], [6].
-
-
-\headtwo{Complexity}For the old approach, we show that the
-complexity of the intersection problem is $O(n^{3})$, the same
-as the complexity of the numerical computations. For the
-new approach, the complexity of the second part is reduced to
-$O(n^{2} (\log n)^{2})$.
-
-To our knowledge, the m-tree previously has not been applied in this
-fashion to the numerical factorization, but it has been used,
-directly or indirectly, in several optimal order algorithms for
-computing the fill-in during the symbolic factorization phase
-[4] - [10], [5], [6]. In \S 1.3., we analyze the complexity of the old and new
-approaches to the intersection problem for the special case of
-an $n \times n$ grid ordered by nested dissection. The special
-structure of this problem allows us to make exact estimates of
-the complexity. To our knowledge, the m-tree previously has not been applied in
-this
-fashion to the numerical factorization, but it has been used,
-directly or indirectly, in several optimal order algorithms for
-computing the fill-in during the symbolic factorization phase
-[4] - [10], [5], [6].
-
-% The command \Refs sets the word Reference as a heading and allows the proper
-% amount of space before the start of the references. Each reference must
-% begin with \ref\\. The article or title of the reference should be in
-% italic. Use the \it command within brackets. End each reference with
-% \endref and allow two returns between references. Use the command
-% \sameauthor (see reference 8) when the same author or group of authors
-% is listed consecutively.
-
-\Refs
-
-\ref 1\\R.~E. Bank, {\it PLTMG users' guide, edition 5.0}, tech. report,
- Department of Mathematics, University of California, San Diego, CA,
-1988.\endref
-
-\ref 2\\R.~E. Bank, T.~F. Dupont, and H.~Yserentant, {\it The hierarchical basis
- multigrid method}, Numer. Math., 52 (1988), pp.~427--458.\endref
-
-\ref 3\\R.~E. Bank and R.~K. Smith, {\it General sparse elimination requires no
- permanent integer storage}, SIAM J. Sci. Stat. Comput., 8 (1987),
- pp.~574--584.\endref
-
-\ref 4\\S.~C. Eisenstat, M.~C. Gursky, M.~Schultz, and A.~Sherman, {\it
- Algorithms and data structures for sparse symmetric gaussian elimination},
- SIAM J. Sci. Stat. Comput., 2 (1982), pp.~225--237.\endref
-
-\ref 5\\A.~George and J.~Liu, {\it Computer Solution of Large Positive
- Definite Systems}, Prentice Hall, Englewood Cliffs, NJ, 1981.\endref
-
-\ref 6\\K.~H. Law and S.~J. Fenves, {\it A node addition model for symbolic
- factorization}, ACM TOMS, 12 (1986), pp.~37--50.\endref
-
-\ref 7\\J.~W.~H. Liu, {\it A compact row storage scheme for factors
- using elimination trees}, ACM TOMS, 12 (1986), pp.~127--148.\endref
-
-\ref 8\\\sameauthor , {\it The role of
- elimination trees in sparse factorization}, Tech. Report CS-87-12,Department
- of Computer Science, York University, Ontario, Canada, 1987.\endref
-
-\ref 9\\D.~J. Rose, {\it A graph theoretic study of the numeric solution of
- sparse positive definite systems}, in Graph Theory and Computing,
- Academic Press, New York, 1972.\endref
-
-\ref 10\\D.~J. Rose, R.~E. Tarjan, and G.~S. Lueker, {\it Algorithmic aspects of
- vertex elimination on graphs}, SIAM J. Comput., 5 (1976), pp.~226--283.\endref
-\enddoublecolumns
-
-\bye
-%%
-%%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%% CUT HERE %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%
-%
-%%%%%%%%%%%%%%%%%%%%%%%%%% ptexpprt.sty %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%
-% This is a file of macros and definitions for creating a chapter
-% for publication in the ACM/SIAM Preprint Series using Plain TeX.
-% This file may be freely distributed but may not be altered in any way.
-% Any comments or questions regarding these macros should be directed to:
-
-% Corey Gray
-% SIAM
-% 3600 University City Science Center
-% Philadelphia, PA 19104-2688
-% USA
-% Telephone: (215) 382-9800
-% Fax: (215) 386-7999
-% e-mail: siampubs@wharton.upenn.edu
-
-%
-
-% Report the version.
-\message{*** ACM/SIAM Plain TeX Preprint Series macro package, version 1.0,
-September 24, 1990.***}
-
-% Make the @ sign a letter for internal control sequences.
-\catcode`\@=11
-%
-%
-%
-
-
-
-%%% DIMENSIONS %%%
-
-\newdimen\pagewidth
-\hsize=41pc
-\pagewidth=\hsize
-\newdimen\pageheight
-\vsize=50pc
-\pageheight=\vsize
-\newdimen\ruleht
-\ruleht=.5pt
-\maxdepth=2.2pt
-
-\parindent=18truept
-\def\firstpar{\parindent=0pt\global\everypar{\parindent=18truept}}
-\parskip=0pt plus 1pt
-
-
-%%% FONTS %%%
-
-\font\tenrm=cmr10
-\font\tenbf=cmbx10
-\font\tenit=cmti10
-\font\tensmc=cmcsc10
-\def\tenpoint{%
- \def\rm{\tenrm}\def\bf{\tenbf}%
- \def\it{\tenit}\def\smc{\tensmc}
- \textfont0=\tenrm \scriptfont0=\sevenrm
- \textfont1=\teni \scriptfont1=\seveni
- \textfont2=\tensy \scriptfont2=\sevensy
- \textfont3=\tenex \scriptfont3=\tenex
-\baselineskip=12pt\rm}%
-
-\font\ninerm=cmr9
-\font\ninebf=cmbx9
-\font\nineit=cmti9
-\def\ninepoint{%
- \def\rm{\ninerm}\def\bf{\ninebf}%
- \def\it{\nineit}\baselineskip=11pt\rm}%
-
-\font\eightrm=cmr8
-\font\eightbf=cmbx8
-\font\eightit=cmti8
-\font\eighti=cmmi8
-\font\eightsy=cmsy8
-\def\eightpoint{%
- \def\rm{\eightrm}\def\bf{\eightbf}%
- \def\it{\eightit}\def\smc{\eightrm}\baselineskip=10pt\rm%
- \textfont0=\eightrm \scriptfont0=\sixrm
- \textfont1=\eighti \scriptfont1=\sixi
- \textfont2=\eightsy \scriptfont2=\sixsy
- \textfont3=\tenex \scriptfont3=\tenex
-}
-
-\font\sixrm=cmr6
-\font\sixbf=cmbx6
-\font\sixi=cmmi6
-\font\sixsmc=cmr5
-\font\sixsy=cmsy6
-\def\sixpoint{%
- \def\rm{\sixrm}\def\bf{\sixbf}%
- \def\smc{\sixsmc}\baselineskip=8pt\rm}%
-
-\fontdimen13\tensy=2.6pt
-\fontdimen14\tensy=2.6pt
-\fontdimen15\tensy=2.6pt
-\fontdimen16\tensy=1.2pt
-\fontdimen17\tensy=1.2pt
-\fontdimen18\tensy=1.2pt
-
-\font\eightrm=cmr8
-\font\ninerm=cmr9
-\font\twelverm=cmr10 scaled\magstep1
-\font\twelvebf=cmbx10 scaled\magstep 1
-\font\sixteenrm=cmr10 scaled\magstep2
-\def\titlefont{\sixteenrm}
-\def\chapterfont{\twelvebf}
-\def\authorfont{\twelverm}
-\def\rheadfont{\tenrm}
-\def\smc{\tensmc}
-
-
-
-
-%%% COUNTERS FOR HEADINGS %%%
-
-\newcount\headcount
-\headcount=1
-\newcount\seccount
-\seccount=1
-\newcount\subseccount
-\subseccount=1
-\def\reset{\global\seccount=1}
-\global\headcount=0
-
-%%% HEADINGS %%%
-
-\def\headone#1{\global\advance\headcount by 1
-\vskip12truept\parindent=0pt{\tenpoint\bf\the\headcount
-\hskip11truept #1.}\par\nobreak\firstpar\global\advance\headcount by 0
- %\global\advance\seccount by 1
-\reset\vskip2truept}
-
-\def\headtwo#1{%\advance\seccount by -1%
- \vskip12truept\parindent=0pt{\tenpoint\bf\the\headcount.%
- \the\seccount\hskip11truept #1.}\enspace\ignorespaces\firstpar
- \global\advance\headcount by 0\global\advance\seccount by 1}
-% \global\advance\subseccount by 1}
-
-
-%%% THEOREMS, PROOFS, DEFINITIONS, etc. %%%
-
-\def\thm#1{{\smc
-#1\enspace}
-\begingroup\it\ignorespaces\firstpar}
-
-\let\lem=\thm
-\let\cor=\thm
-\let\prop=\thm
-
-\def\endthm{\endgroup}
-\let\endlem=\endthm
-\let\endcor=\endthm
-\let\endprop=\endthm
-
-\def\prf#1{{\it #1.}\rm\enspace\ignorespaces}
-\let\rem=\prf
-\let\case=\prf
-
-
-\def\dfn#1{{\smc
-#1\enspace}
-\rm\ignorespaces}
-
-
-
-%%% FIGURES AND CAPTIONS %%%
-
-\def\caption#1\endcaption{\vskip18pt\ninerm\centerline{#1}\vskip18pt\tenrm}
-
-\newinsert\topins \newif\ifp@ge \newif\if@mid
-\def\topinsert{\@midfalse\p@gefalse\@ins}
-\def\midinsert{\@midtrue\@ins}
-\def\pageinsert{\@midfalse\p@getrue\@ins}
-\skip\topins=0pt %no space added when a topinsert is present
-\count\topins=1000 %magnification factor (1 to 1)
-\dimen\topins=\maxdimen
-\def\@ins{\par\begingroup\setbox0=\vbox\bgroup}
-\def\endinsert{\egroup
- \if@mid \dimen@=\ht0 \advance\dimen@ by\dp0
- \advance\dimen@ by12\p@ \advance\dimen@ by\pagetotal
- \ifdim\dimen@>\pagegoal \@midfalse\p@gefalse\fi\fi
- \if@mid \bigskip \box0 \bigbreak
- \else\insert\topins{\penalty100
- \splittopskip=0pt \splitmaxdepth=\maxdimen \floatingpenalty=0
- \ifp@ge \dimen@=\dp0
- \vbox to\vsize{\unvbox0 \kern-\dimen@}
- \else \box0 \nobreak\bigskip\fi}\fi\endgroup}
-
-
-%%% REFERENCES %%%
-
-\newdimen\refindent@
-\newdimen\refhangindent@
-\newbox\refbox@
-\setbox\refbox@=\hbox{\ninepoint\rm\baselineskip=11pt [00]}% Default 2 digits
-\refindent@=\wd\refbox@
-
-\def\resetrefindent#1{%
- \setbox\refbox@=\hbox{\ninepoint\rm\baselineskip=11pt [#1]}%
- \refindent@=\wd\refbox@}
-
-\def\Refs{%
- \unskip\vskip1pc
- \leftline{\noindent\tenpoint\bf References}%
- \penalty10000
- \vskip4pt
- \penalty10000
- \refhangindent@=\refindent@
- \global\advance\refhangindent@ by .5em
- \global\everypar{\hangindent\refhangindent@}%
- \parindent=0pt\ninepoint\rm}
-
-\def\sameauthor{\leavevmode\vbox to 1ex{\vskip 0pt plus 100pt
- \hbox to 2em{\leaders\hrule\hfil}\vskip 0pt plus 300pt}}
-
-\def\ref#1\\#2\endref{\leavevmode\hbox to \refindent@{\hfil[#1]}\enspace #2\par}
-
-
-%%% OUTPUT %%%
-
-\newinsert\margin
-\dimen\margin=\maxdimen
-\count\margin=0 \skip\margin=0pt
-
-
-\def\footnote#1{\edef\@sf{\spacefactor\the\spacefactor}#1\@sf
- \insert\footins\bgroup\eightpoint\hsize=30pc
- \interlinepenalty100 \let\par=\endgraf
- \leftskip=0pt \rightskip=0pt
- \splittopskip=10pt plus 1pt minus 1pt \floatingpenalty=20000
-\smallskip
-\item{#1}\bgroup\strut\aftergroup\@foot\let\next}
-\skip\footins=6pt plus 2pt minus 4pt
-\dimen\footins=30pc
-
-\newif\iftitle
-
-
-\def\titlepage{\global\titletrue\footline={\hss\ninepoint\rm\folio\hss}}
-\def\rhead{\ifodd\pageno CHAPTER TITLE
- \else AUTHORS NAMES\fi}
-
-\def\makefootline{\ifnum\pageno>1\global\footline={\hfill}\fi
- \baselineskip24\p@\vskip12\p@\fullline{\the\footline}}
-\def\leftheadline{\hbox to \pagewidth{
- \vbox to 10pt{}
- {\kern-8pt\tenrm\folio\hfill\ninerm\rhead}}}
-\def\rightheadline{\hbox to \pagewidth{
- \vbox to 10pt{}
- \kern-8pt\ninerm\rhead\hfil
- {\kern-1pc\tenrm\folio}}}
-
-\def\onepageout#1{\shipout\vbox{
-\offinterlineskip
- \vbox to 2.25pc{%
- \iftitle \global\titlefalse
-% \setcornerrules
- \else\ifodd\pageno\rightheadline\else\leftheadline\fi\fi \vfill}
-\vbox to \pageheight{
- \ifvoid\margin\else
- \rlap{\kern31pc\vbox to0pt{\kern4pt\box\margin \vss}}\fi
- #1 %
-\ifvoid\footins\else
- \vskip\skip\footins \kern 0pt
- \hrule height\ruleht width 2.5pc \kern-\ruleht \kern 0pt
- \unvbox\footins\fi
-\boxmaxdepth=\maxdepth}}
-\advancepageno}
-
-\def\setcornerrules{\hbox to \pagewidth{
- \vrule width 1pc height\ruleht \hfil \vrule width 1pc}
- \hbox to \pagewidth{\llap{\sevenrm(page \folio)\kern1pc}
- \vrule height1pc width\ruleht depth0pt
- \hfil \vrule width\ruleht depth0pt}}
-\output{\onepageout{\unvbox255}}
-
-\newbox\partialpage
-\def\begindoublecolumns{\begingroup
- \output={\global\setbox\partialpage=\vbox{\unvbox255\bigskip}}\eject
- \output={\doublecolumnout} \hsize=20pc \vsize=101pc}
-\def\enddoublecolumns{\output={\balancecolumns}\eject
- \endgroup \pagegoal=\vsize}
-
-\def\doublecolumnout{\splittopskip=\topskip \splitmaxdepth=\maxdepth
- \dimen@=50pc \advance\dimen@ by-\ht\partialpage
- \setbox0=\vsplit255 to\dimen@ \setbox2=\vsplit255 to\dimen@
- \onepageout\pagesofar \unvbox255 \penalty\outputpenalty}
-\def\pagesofar{\unvbox\partialpage
- \wd0=\hsize \wd2=\hsize \hbox to\pagewidth{\box0\hfil\box2}}
-\def\balancecolumns{\setbox0=\vbox{\unvbox255} \dimen@=\ht0
- \advance\dimen@ by\topskip \advance\dimen@ by-\baselineskip
- \divide\dimen@ by2 \splittopskip=\topskip
-{\vbadness=10000 \loop \global\setbox3=\copy0
- \global\setbox1=\vsplit3 to\dimen@
- \ifdim\ht3>\dimen@ \global\advance\dimen@ by1pt \repeat}
- \setbox0=\vbox to\dimen@{\unvbox1} \setbox2=\vbox to\dimen@{\unvbox 3}
-\pagesofar}
-
-
-
-
-% Turn off @ as being a letter.
-%
-\catcode`\@=13
-
-% End of ptexpprt.sty
-
-
-CUT HERE............
diff --git a/Master/texmf-dist/source/latex/siam/ptexproc.all b/Master/texmf-dist/source/latex/siam/ptexproc.all
deleted file mode 100644
index 728b5da243d..00000000000
--- a/Master/texmf-dist/source/latex/siam/ptexproc.all
+++ /dev/null
@@ -1,704 +0,0 @@
-
-
-This file constitutes the full distribution of SIAM Proceedings Series
-Plain TeX macros. The files are:
-
-ptexproc.tex (An example file, also containing documentation)
-
-ptexproc.sty (the style file)
-
-To use these macros, separate at the indicated cut lines.
-
-%%%%%%%%%%%%%%%%%%%%%%%%%CUT HERE%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-% This is ptexproc.tex, an example file for use with the SIAM Plain TeX
-% Proceedings Series macros. Comments are placed at the beginning and
-% throughout this file. Please take the time to read them as they document
-% how to use these macros. This file can be composed and printed out for
-% use as sample output. Please ignore the underfull \vbox on page 3.
-
-% Any comments or questions regarding these macros should be directed to:
-%
-% Corey Gray
-% SIAM
-% 3600 University City Science Center
-% Philadelphia, PA 19104-2688
-% USA
-% Telephone: (215) 382-9800
-% Fax: (215) 386-7999
-% e-mail: gray@siam.org
-
-
-% This file is to be used as an example for style only. It should not be read
-% for content.
-
-%%%%%%%%%%%%%%% PLEASE NOTE THE FOLLOWING STYLE RESTRICTIONS %%%%%%%%%%%%%%%
-
-%% 1. You must use the numbered reference style([1],[2]), listing the
-%% references at the end of the chapter either by order of citation
-%% or alphabetically.
-%%
-%% 2. This macro is set up for three levels of headings. Use the commands
-%% \headone, \headtwo, and \headthree. The macro will automatically
-%% number the headings.
-%%
-%% 3. The running heads are defined by the commands \def\leftrh{} and
-%% \def\rightrh{}. You must fill in the empty field of these commands
-%% with the appropriate information. The left running head should be the
-%% authors names. For papers with multiple authors, please follow these
-%% rules; for two authors type {Author 1 and Author 2}; for more than two
-%% authors type {Author 1 et al.}. The right running head is the title of
-%% the paper. If the title is more than 50 characters, including spaces,
-%% please provide a shortened version. All information should be typed
-%% initial cap and lower case.
-%%
-%% 5. Theorems, Lemmas, Definitions, etc. are to be double-numbered,
-%% indicating the section and the occurrence of that element
-%% within that section. (For example, the first theorem in the second
-%% section would be numbered 2.1.) This numbering must
-%% be done manually.
-%%
-%% 6. Proofs are handled by \prf\endprf. If you want to use an end-of-proof
-%% box, insert \qed right before the \endprf command.
-%%
-%% 7. Figures and equations must be manually single-numbered. Use \leqno
-%% for equation numbering. The macro provides the \fig for including
-%% figures. This command consists of three fields. The first field is
-%% used for inserting the appropriate space for the figure. The second
-%% field is the figure number. The third field is the caption. See the
-%% example included in this file. SIAM supports the use of psfig for
-%% including Postscript figures. All Postscript figures should be sent
-%% as separate files. A hardcopy version of all Postscript figures is
-%% also required. See note regarding this under How to Submit Your Paper.
-%%
-%% 8. Use of \title\endtitle and \lasttitle\endlastitle.
-%% This macro package provides two possible commands for handling the
-%% title of your paper. The commands \title\endtitle should be used for
-%% all lines except the last line of multiple line titles. The commands
-%% \lasttitle\endlasttitle should be used for the last line of multiple
-%% line titles. In the case of a single line title, \lasttitle\endlasttitle
-%% should be used.
-%%
-%% 9. Use of \author\endauthor and \lastauthor\endlastauthor.
-%% As in the title macro, two possible commands are provided for the
-%% author. The commands \author\endauthor should be used for the first
-%% line of authors if there are more than one line. The commands
-%% \lastauthor\endlastauthor should be used for the last line
-%% of multiple lines of authors. In the case of a single line of authors,
-%% \lastauthor\endlastauthor should be used. A maximum of four authors
-%% should be placed on any one line. The appropriate space must also be
-%% hard coded between authors on the same line. The spacing is as follows:
-%%
-%% If 2 authors; \hskip4pc between
-%% If 3 authors; \hskip3pc between
-%% If 4 authors; \hskip2pc between
-%%
-%% 10. Grant information and author affiliations.
-%% This information is included by using the \footnote command and the
-%% appropriate footnote symbol. SIAM uses footnote symbols in a
-%% particular order. Below is a list of these symbols:
-%%
-%% asterisk
-%% single-dagger
-%% double-dagger
-%% section sign
-%% paragraph
-%% parallel
-%% double asterisk
-%% double single-dagger
-%% double double-dagger
-%%
-%% For illustrative purposes, all footnote symbols have been used in the
-%% example file.
-%%
-%% A note regarding \footnote. This command seems to leave extra white
-%% space between footnotes. This is quite evident in the example file. If
-%% any user of these macros has a solution to this problem, I would
-%% appreciate hearing from you. Send your comments to: gray@siam.org.
-%%
-%% The following general rules apply for including grants and affiliations:
-%% a) If there is a single grant for the paper, then the grant
-%% information should be footnoted to the title.
-%% b) If there is more than one grant, included the grant information
-%% with each authors affiliation.
-%% c) If there are different grants for the paper but the authors share
-%% the same affiliation, footnote the grant information to the title.
-%% For example, The work of the first author was supported by xyz.
-%% The work of the second author was supported by abc. And so on.
-%%
-%%
-%% 11. Special fonts.
-%% SIAM supports the use of AMS-TeX fonts version 2.0 and later. As
-%% described in the manual for these fonts, they can be included by
-%% \input{amssym.def} and \input{amssym.tex}.
-%%
-%% 12. How to Submit Your Paper.
-%% The electronic version of your paper should be sent to proceed@siam.org.
-%% A hardcopy version should also be submitted. Instructions are included
-%% in your acceptance letter. Please be sure to send hardcopy
-%% versions of any Postscript figures you have submitted electronically.
-%% Be sure to return your signed Copyright Transfer Agreement. We cannot
-%% publish your paper without one.%%
-%%
-%%
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-\input ptexproc.sty
-
-\def\leftrh{Gray et al.}
-\def\rightrh{SIAM Proceedings Series Macros}
-
-\startchapter %Place this command at the beginning of the file immediately
- %after the \input command.
-
-
-
-\title Chapter 1\endtitle
-\title SIAM Proceedings Series Macros\endtitle
-\lasttitle for Use with Plain TeX\footnote*{Any information
-regarding grants should be placed here.}\endlasttitle
-
-\author J. Corey Gray\footnote{$^{\dag}$}{Production Manager, Society for
-Industrial and Applied Mathematics, Philadelphia, PA.}
-\hskip2truepc Tricia Manning\footnote{$^{\ddag}$}{Publications
-Specialist, Society for Industrial and Applied Mathematics, Philadelphia,
-PA.}
-\hskip2truepc Vickie Kearn\footnote{$^{\S}$}{Publisher, Society for Industrial
-and Applied Mathematics, Philadelphia, PA.}
-\hskip2truepc Nancy Abbott\footnote{$^{\P}$}{Design Supervisor, Society for
-Industrial and Applied Mathematics, Philadelphia, PA.}
-\endauthor
-\lastauthor Sue Ciambrano\footnote{$^{\parallel}$}{Acquisition Editor, Society for
-Industrial and Applied Mathematics, Philadelphia, PA.}
-\hskip2truepc Paul Duggan\footnote{$^{**}$}{Composition
-Specialist, Society for Industrial and Applied Mathematics, Philadelphia,
-PA.}
-\hskip2truepc Robbi Anne Albert\footnote{$^{\dagger\dagger}$}{Production,
-Assistant, Society for Industrial
-and Applied Mathematics, Philadelphia, PA.}
-\hskip2truepc Jean Anderson\footnote{$^{\ddag\ddag}$}{Composition Coordinator, Society for
-Industrial and Applied Mathematics, Philadelphia, PA.}
-\endlastauthor
-
-% Use \headone for the first level headings. The macro will automatically
-% number the headings.
-
-\centerline{\bf Abstract}
-\abstract An equivalence is shown between realizability of input/output (i/o) operators by
-rational control systems and high-order algebraic differential equations for
-i/o pairs. This generalizes, to nonlinear systems, the equivalence
-between autoregressive representations and finite dimensional linear
-realizability.\endabstract
-
-
-\headone{Problem Specification}
-In this paper, we consider the solution of the $N \times N$ linear
-system
-$$A x = b\leqno (1)$$
-where $A$ is large, sparse, symmetric, and positive definite. We consider
-the direct solution of by means of general sparse Gaussian
-elimination. In such a procedure, we find a permutation matrix $P$, and
-compute the decomposition
-$$
-P A P^{t} = L D L^{t}
-\leqno (2)$$
-
-\noindent where $L$ is unit lower triangular and $D$ is diagonal.
-
-
-\headone{Design Considerations}
-Several good ordering algorithms (nested dissection and minimum degree)
-are available for computing $P$ [1], [2].
-Since our interest here does not
-focus directly on the ordering, we assume for convenience that $P=I$,
-or that $A$ has been preordered to reflect an appropriate choice of $P$.
-
-% Use \thm and \endthm for theorems. They must be numbered manually.
-% Lemmas (\lem \endlem), corollaries (\cor \endcor), and
-% propositions (\prop \endprop) are coded the same as theorems and must
-% also be numbered manually.
-
-\thm{Theorem 2.1.} The method was extended to three
-dimensions. For the standard multigrid
-coarsening
-(in which, for a given grid, the next coarser grid has $1/8$
-as many points), anisotropic problems require plane
-relaxation to
-obtain a good smoothing factor.\endthm
-
-Several good ordering algorithms (nested dissection and minimum degree)
-are available for computing $P$ [1], [2].
-Since our interest here does not
-focus directly on the ordering, we assume for convenience that $P=I$,
-or that $A$ has been preordered to reflect an appropriate choice of $P$.
-Several good ordering algorithms (nested dissection and minimum degree)
-are available for computing $P$ [1], [2].
-Since our interest here does not
-focus directly on the ordering, we assume for convenience that $P=I$,
-or that $A$ has been preordered to reflect an appropriate choice of $P$.
-
-% Use \prf and \endprf to begin and end a proof.
-% The use of \qed will produce an end-of-proof box.
-
-\prf{Proof} In this paper we consider two methods. The first method
-is
-basically the method considered with two differences:
-first, we perform plane relaxation by a two-dimensional
-multigrid method, and second, we use a slightly different
-choice of
-interpolation operator, which improves performance
-for nearly singular problems. In the second method coarsening
-is done by successively coarsening each.\qed\endprf
-
-% Use \dfn and \enddfn to begin and end definitions.
-
-\dfn{Definition 2.1.}We describe the two methods in \S\ 1.2. This is a
-definition in the plain tex macro.\enddfn
-
-This is accomplished by exploiting the m-tree,
-a particular spanning tree for the graph of the filled-in matrix.
-Our purpose here is to examine the nonnumerical complexity of the
-sparse elimination algorithm given in [3].
-As was shown there, a general sparse elimination scheme based on the
-bordering algorithm requires less storage for pointers and
-row/column indices than more traditional implementations of general
-sparse elimination. This is accomplished by exploiting the m-tree,
-a particular spanning tree for the graph of the filled-in matrix.
-
-
-Our purpose here is to examine the nonnumerical complexity of the
-sparse elimination algorithm given in [3].
-As was shown there, a general sparse elimination scheme based on the
-bordering algorithm requires less storage for pointers and
-row/column indices than more traditional implementations of general
-sparse elimination. This is accomplished by exploiting the m-tree,
-a particular spanning tree for the graph of the filled-in matrix.
-Since our interest here does not
-focus directly on the ordering, we assume for convenience that $P=I$,
-or that $A$ has been preordered to reflect an appropriate choice of $P$.
-
-% Use \lem and \endlem to begin and end lemmas.
-
-\lem{Lemma 2.1.}We discuss first the choice for $I_{k-1}^k$
-which is a generalization. We assume that $G^{k-1}$ is
-obtained
-from $G^k$
-by standard coarsening; that is, if $G^k$ is a tensor product
-grid $G_{x}^k \times G_{y}^k \times G_{z}^k$,
-$G^{k-1}=G_{x}^{k-1} \times G_{y}^{k-1} \times G_{z}^{k-1}$,
-where $G_{x}^{k-1}$ is obtained by deleting every other grid
-point of $G_x^k$ and similarly for $G_{y}^k$ and $G_{z}^k$.
-\endlem
-
-% Use \fig to insert space for figures .
-
-\fig{10pc}{Fig. 1}{This is the caption for figure one.}
-
-To our knowledge, the m-tree previously has not been applied in this
-fashion to the numerical factorization, but it has been used,
-directly or indirectly, in several optimal order algorithms for
-computing the fill-in during the symbolic factorization phase
-[4] - [10], [5], [6]. In \S 1.3., we analyze the complexity of the old and new
-approaches to the intersection problem for the special case of
-an $n \times n$ grid ordered by nested dissection. The special
-structure of this problem allows us to make exact estimates of
-the complexity. To our knowledge, the m-tree previously has not been applied in this
-fashion to the numerical factorization, but it has been used,
-directly or indirectly, in several optimal order algorithms for
-computing the fill-in during the symbolic factorization phase
-[4] - [10], [5], [6].
-
-% Use \headtwo for second level headings. They will be numbered automatically.
-
-\headtwo{Robustness}In \S 1.2, we review the bordering algorithm, and introduce
-the sorting and intersection problems that arise in the
-sparse formulation of the algorithm.
-
-\headtwo{Versatility} In \S 1.3., we analyze the complexity of the old and new
-approaches to the intersection problem for the special case of
-an $n \times n$ grid ordered by nested dissection. The special
-structure of this problem allows us to make exact estimates of
-the complexity. To our knowledge, the m-tree previously has not been applied in this
-fashion to the numerical factorization, but it has been used,
-directly or indirectly, in several optimal order algorithms for
-computing the fill-in during the symbolic factorization phase
-[4] - [10], [5], [6].
-
-
-% Use \headthree for third level headings.
-
-\headthree{Complexity.}For the old approach, we show that the
-complexity of the intersection problem is $O(n^{3})$, the same
-as the complexity of the numerical computations. For the
-new approach, the complexity of the second part is reduced to
-$O(n^{2} (\log n)^{2})$.
-
-% The command \Refs sets the word Reference as a heading and allows the proper
-% amount of space before the start of the references. Each reference must
-% begin with \ref\\. The article or title of the reference should be in
-% italic. Use the \it command within brackets. End each reference with
-% \endref and allow two returns between references. Use the command
-% \sameauthor (see reference 8) when the same author or group of authors
-% is listed consecutively.
-
-\Refs
-
-\ref 1\\R.~E. Bank, {\it PLTMG users' guide, edition 5.0}, tech. report,
- Department of Mathematics, University of California, San Diego, CA, 1988.\endref
-
-\ref 2\\R.~E. Bank, T.~F. Dupont, and H.~Yserentant, {\it The hierarchical basis
- multigrid method}, Numer. Math., 52 (1988), pp.~427--458.\endref
-
-\ref 3\\R.~E. Bank and R.~K. Smith, {\it General sparse elimination requires no
- permanent integer storage}, SIAM J. Sci. Stat. Comput., 8 (1987),
- pp.~574--584.\endref
-
-\ref 4\\S.~C. Eisenstat, M.~C. Gursky, M.~Schultz, and A.~Sherman, {\it
- Algorithms and data structures for sparse symmetric gaussian elimination},
- SIAM J. Sci. Stat. Comput., 2 (1982), pp.~225--237.\endref
-
-\ref 5\\A.~George and J.~Liu, {\it Computer Solution of Large Sparse Positive
- Definite Systems}, Prentice Hall, Englewood Cliffs, NJ, 1981.\endref
-
-\ref 6\\K.~H. Law and S.~J. Fenves, {\it A node addition model for symbolic
- factorization}, ACM TOMS, 12 (1986), pp.~37--50.\endref
-
-\ref 7\\J.~W.~H. Liu, {\it A compact row storage scheme for cholesky factors
- using elimination trees}, ACM TOMS, 12 (1986), pp.~127--148.\endref
-
-\ref 8\\\sameauthor , {\it The role of
- elimination trees in sparse factorization}, Tech. Report CS-87-12,Department
- of Computer Science, York University, Ontario, Canada, 1987.\endref
-
-\ref 9\\D.~J. Rose, {\it A graph theoretic study of the numeric solution of
- sparse positive definite systems}, in Graph Theory and Computing,
- Academic Press, New York, 1972.\endref
-
-\ref 10\\D.~J. Rose, R.~E. Tarjan, and G.~S. Lueker, {\it Algorithmic aspects of
- vertex elimination on graphs}, SIAM J. Comput., 5 (1976), pp.~226--283.\endref
-
-
-\bye
-
-%end of example file
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%CUT HERE%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-% This is ptexproc.sty
-% This file may be freely distributed but may not be altered in any way.
-% Any comments or questions regarding these macros should be directed to:
-
-% Corey Gray
-% SIAM
-% 3600 University City Science Center
-% Philadelphia, PA 19104-2688
-% USA
-% Telephone: (215) 382-9800
-% Fax: (215) 386-7999
-% e-mail: gray@siam.org
-
-%
-% This is a file of macros and definitions for creating a chapter
-% for publication in the SIAM Proceedings Series using Plain TeX.
-
-% Report the version.
-\message{*** SIAM Plain TeX Proceedings Series macro package, version 1.0,
-November 6, 1992.***}
-
-% Make the @ sign a letter for internal control sequences.
-\catcode`\@=11
-%
-%
-%
-
-\overfullrule=0pt
-\baselineskip=14truept
-
-
-%%% DIMENSIONS %%%
-
-\hsize=36truepc
-\vsize=55truepc
-%\hoffset=.5in
-\parindent=18truept
-\def\firstpar{\parindent=0pt\global\everypar{\parindent=18truept}}
-\parskip=0pt
-
-
-%%% FONTS %%%
-
-\font\tenrm=cmr10
-\font\tenbf=cmbx10
-\font\tenit=cmti10
-\font\tensmc=cmcsc10
-\def\tenpoint{%
- \def\rm{\tenrm}\def\bf{\tenbf}%
- \def\it{\tenit}\def\smc{\tensmc}
- \textfont0=\tenrm \scriptfont0=\sevenrm
- \textfont1=\teni \scriptfont1=\seveni
- \textfont2=\tensy \scriptfont2=\sevensy
- \textfont3=\tenex \scriptfont3=\tenex
-\baselineskip=12pt\rm}%
-
-\font\ninerm=cmr9
-\font\ninebf=cmbx9
-\font\nineit=cmti9
-\def\ninepoint{%
- \def\rm{\ninerm}\def\bf{\ninebf}%
- \def\it{\nineit}\baselineskip=11pt\rm}%
-
-\font\eightrm=cmr8
-\font\eightbf=cmbx8
-\font\eightit=cmti8
-\font\eighti=cmmi8
-\font\eightsy=cmsy8
-\def\eightpoint{%
- \def\rm{\eightrm}\def\bf{\eightbf}%
- \def\it{\eightit}\def\smc{\eightrm}\baselineskip=10pt\rm%
- \textfont0=\eightrm \scriptfont0=\sixrm
- \textfont1=\eighti \scriptfont1=\sixi
- \textfont2=\eightsy \scriptfont2=\sixsy
- \textfont3=\tenex \scriptfont3=\tenex
-}
-
-\font\sixrm=cmr6
-\font\sixbf=cmbx6
-\font\sixi=cmmi6
-\font\sixsmc=cmr5
-\font\sixsy=cmsy6
-\def\sixpoint{%
- \def\rm{\sixrm}\def\bf{\sixbf}%
- \def\smc{\sixsmc}\baselineskip=8pt\rm}%
-
-\fontdimen13\tensy=2.6pt
-\fontdimen14\tensy=2.6pt
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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,
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-\def\ps@myheadings{\let\@mkboth\@gobbletwo
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- \def\@oddhead{\rlap{\normalsize\rm\rightmark}\hfil{small\thepage}}%
- \def\@evenhead%{\hfil{\small\@chapapp}\
- {\small\thepage}\hfil\llap{\normalsize\rm\leftmark}}%
- \def\chaptermark##1{}%
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-\def\theequation{\arabic{section}.\arabic{equation}}
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-\def\section{\@startsection{section}{1}{0pt}{-12pt}{3pt}{\hyphenpenalty=\@M
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-\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
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-
-\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
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-
-\def\@ynalg#1#2{\expandafter\@ifdefinable\csname #1\endcsname
-{\@definecounter{#1}%
-\expandafter\xdef\csname the#1\endcsname{\@thmcounter{#1}}%
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-
-\def\@oalg#1[#2]#3{\expandafter\@ifdefinable\csname #1\endcsname
- {\global\@namedef{the#1}{\@nameuse{the#2}}%
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-\def\@yalg#1#2[#3]{\@opargbeginalgorithm{#2}{\csname
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-
-
-
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-\def\@beginproof#1{\rm \trivlist \item[\hskip \labelsep{\it #1.\/}]}
-\def\@endproof{\outerparskip 0pt\endtrivlist}
-
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-\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.}]}
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-%\def\@enddefinition{\outerparskip 0pt\endtrivlist}
-
-
-\def\@beginalgorithm#1#2{\rm \trivlist \item[\hskip \labelsep{\sc #1\ #2.}]}
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-
-\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}}
-
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-\newtheorem{axiom}{Axiom}[section]
-\newtheorem{cond}{Condition}[section]
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-
-\newtheorem{Conjecture}{Conjecture}[section]
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-
-\newproof{Example}{Example}
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-
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-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% %%
-%% BIBLIOGRAPHY %%
-%% %%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-
-\def\thebibliography#1{%
-%\cleardoublepage
-\parindent 0em
-\vspace{6pt}
-\begin{flushleft}\normalsize\bf References\end{flushleft}
-\addvspace{3pt}\nopagebreak\list
- %% default is no labels, for those not using \cite or BibTeX
-% {[\arabic{enumi}]} {\settowidth\labelwidth{[#1]}
-{[\arabic{enumi}]}{\settowidth\labelwidth{mm}
-\leftmargin\labelwidth
- \advance\leftmargin\labelsep
- \usecounter{enumi}\@bibsetup}
-\def\newblock{\hskip .11em plus .33em minus -.07em}
- \sloppy\clubpenalty4000\widowpenalty4000
- \sfcode`\.=1000\relax}
-
-%% setup 8/10 type
-\def\@bibsetup{\itemindent=0pt \itemsep=0pt \parsep=0pt
-\small}
-
-\def\sameauthor{\leavevmode\vrule height 2pt depth -1.6pt width 23pt}
-
-%
-%% End of ltexprt.sty
-%
-%%%%%%%%%%%%%%%%%%%%%%%%% End of soda209.all %%%%%%%%%%%%%%%%%%%%%%%
diff --git a/Master/texmf-dist/source/latex/siam/soda2e.all b/Master/texmf-dist/source/latex/siam/soda2e.all
deleted file mode 100644
index 17f570966fa..00000000000
--- a/Master/texmf-dist/source/latex/siam/soda2e.all
+++ /dev/null
@@ -1,688 +0,0 @@
-%% This is soda2e.all. This file is to be used for creating a paper
-%% in the ACM/SIAM Preprint series with LaTeX2E. It consists of the following
-%% two files:
-%%
-%% ltexpprt.tex ---- an example and documentation file
-%% ltexpprt.sty ---- the macro file
-%%
-%% To use, cut this file apart at the appropriate places. You can run the
-%% example file with the macros to get sample output.
-%%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%% CUT HERE %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%
-%
-%%%%%%%%%%%%%%%%%%%%%%%%%% ltexpprt.tex %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%
-% This is ltexpprt.tex, an example file for use with the SIAM LaTeX2E
-% Preprint Series macros. It is designed to provide double-column output.
-% Please take the time to read the following comments, as they document
-% how to use these macros. This file can be composed and printed out for
-% use as sample output.
-
-% Any comments or questions regarding these macros should be directed to:
-%
-% Corey Gray
-% SIAM
-% 3600 University City Science Center
-% Philadelphia, PA 19104-2688
-% USA
-% Telephone: (215) 382-9800
-% Fax: (215) 386-7999
-% e-mail: gray@siam.org
-
-
-% This file is to be used as an example for style only. It should not be read
-% for content.
-
-%%%%%%%%%%%%%%% PLEASE NOTE THE FOLLOWING STYLE RESTRICTIONS %%%%%%%%%%%%%%%
-
-%% 1. There are no new tags. Existing LaTeX tags have been formatted to match
-%% the Preprint series style.
-%%
-%% 2. You must use \cite in the text to mark your reference citations and
-%% \bibitem in the listing of references at the end of your chapter. See
-%% the examples in the following file. If you are using BibTeX, please
-%% supply the bst file with the manuscript file.
-%%
-%% 3. This macro is set up for two levels of headings (\section and
-%% \subsection). The macro will automatically number the headings for you.
-%%
-%% 5. No running heads are to be used for this volume.
-%%
-%% 6. Theorems, Lemmas, Definitions, etc. are to be double numbered,
-%% indicating the section and the occurence of that element
-%% within that section. (For example, the first theorem in the second
-%% section would be numbered 2.1. The macro will
-%% automatically do the numbering for you.
-%%
-%% 7. Figures, equations, and tables must be single-numbered.
-%% Use existing LaTeX tags for these elements.
-%% Numbering will be done automatically.
-%%
-%%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-
-
-\documentclass[twoside,leqno,twocolumn]{article}
-\usepackage{ltexpprt}
-\begin{document}
-
-
-%\setcounter{chapter}{2} % If you are doing your chapter as chapter one,
-%\setcounter{section}{3} % comment these two lines out.
-
-\title{\Large SIAM/ACM Preprint Series Macros for
-Use With LaTeX\thanks{Supported by GSF grants ABC123, DEF456, and GHI789.}}
-\author{Corey Gray\thanks{Society for Industrial and Applied Mathematics.} \\
-\and
-Tricia Manning\thanks{Society for Industrial and Applied Mathematics.}}
-\date{}
-
-\maketitle
-
-\pagestyle{myheadings}
-\markboth{}{}
-
-
-%\pagenumbering{arabic}
-%\setcounter{page}{1}%Leave this line commented out.
-
-\begin{abstract} \small\baselineskip=9pt This is the text of my abstract. It is a brief
-description of my
-paper, outlining the purposes and goals I am trying to address.\end{abstract}
-
-
-
-
-\section{Problem Specification.}In this paper, we consider the solution of the $N \times
-N$ linear
-system
-\begin{equation} \label{e1.1}
-A x = b
-\end{equation}
-where $A$ is large, sparse, symmetric, and positive definite. We consider
-the direct solution of (\ref{e1.1}) by means of general sparse Gaussian
-elimination. In such a procedure, we find a permutation matrix $P$, and
-compute the decomposition
-\[
-P A P^{t} = L D L^{t}
-\]
-where $L$ is unit lower triangular and $D$ is diagonal.
-
-
-\section{Design Considerations.}Several good ordering algorithms (nested dissection and
-minimum degree)
-are available for computing $P$ \cite{GEORGELIU}, \cite{ROSE72}.
-Since our interest here does not
-focus directly on the ordering, we assume for convenience that $P=I$,
-or that $A$ has been preordered to reflect an appropriate choice of $P$.
-
-Our purpose here is to examine the nonnumerical complexity of the
-sparse elimination algorithm given in \cite{BANKSMITH}.
-As was shown there, a general sparse elimination scheme based on the
-bordering algorithm requires less storage for pointers and
-row/column indices than more traditional implementations of general
-sparse elimination. This is accomplished by exploiting the m-tree,
-a particular spanning tree for the graph of the filled-in matrix.
-
-\begin{theorem} The method was extended to three
-dimensions. For the standard multigrid
-coarsening
-(in which, for a given grid, the next coarser grid has $1/8$
-as many points), anisotropic problems require plane
-relaxation to
-obtain a good smoothing factor.\end{theorem}
-
-Our purpose here is to examine the nonnumerical complexity of the
-sparse elimination algorithm given in \cite{BANKSMITH}.
-As was shown there, a general sparse elimination scheme based on the
-bordering algorithm requires less storage for pointers and
-row/column indices than more traditional implementations of general
-sparse elimination. This is accomplished by exploiting the m-tree,
-a particular spanning tree for the graph of the filled-in matrix.
-Several good ordering algorithms (nested dissection and minimum degree)
-are available for computing $P$ \cite{GEORGELIU}, \cite{ROSE72}.
-Since our interest here does not
-focus directly on the ordering, we assume for convenience that $P=I$,
-or that $A$ has been preordered to reflect an appropriate choice of $P$.
-
-\begin{proof} In this paper we consider two methods. The first method
-is
-basically the method considered with two differences:
-first, we perform plane relaxation by a two-dimensional
-multigrid method, and second, we use a slightly different
-choice of
-interpolation operator, which improves performance
-for nearly singular problems. In the second method coarsening
-is done by successively coarsening in each of the three
-independent variables and then ignoring the intermediate
-grids; this artifice simplifies coding considerably.
-\end{proof}
-
-Our purpose here is to examine the nonnumerical complexity of the
-sparse elimination algorithm given in \cite{BANKSMITH}.
-As was shown there, a general sparse elimination scheme based on the
-bordering algorithm requires less storage for pointers and
-row/column indices than more traditional implementations of general
-sparse elimination. This is accomplished by exploiting the m-tree,
-a particular spanning tree for the graph of the filled-in matrix.
-
-\begin{Definition}{\rm We describe the two methods in \S 1.2. In \S\ 1.3. we
-discuss
-some remaining details.}
-\end{Definition}
-
-Our purpose here is to examine the nonnumerical complexity of the
-sparse elimination algorithm given in \cite{BANKSMITH}.
-As was shown there, a general sparse elimination scheme based on the
-bordering algorithm requires less storage for pointers and
-row/column indices than more traditional implementations of general
-sparse elimination. This is accomplished by exploiting the m-tree,
-a particular spanning tree for the graph of the filled-in matrix.
-Several good ordering algorithms (nested dissection and minimum degree)
-are available for computing $P$ \cite{GEORGELIU}, \cite{ROSE72}.
-Since our interest here does not
-focus directly on the ordering, we assume for convenience that $P=I$,
-or that $A$ has been preordered to reflect an appropriate choice of $P$.
-
-Our purpose here is to examine the nonnumerical complexity of the
-sparse elimination algorithm given in \cite{BANKSMITH}.
-As was shown there, a general sparse elimination scheme based on the
-bordering algorithm requires less storage for pointers and
-row/column indices than more traditional implementations of general
-sparse elimination.
-
-\begin{lemma} We discuss first the choice for $I_{k-1}^k$
-which is a generalization. We assume that $G^{k-1}$ is
-obtained
-from $G^k$
-by standard coarsening; that is, if $G^k$ is a tensor product
-grid $G_{x}^k \times G_{y}^k \times G_{z}^k$,
-$G^{k-1}=G_{x}^{k-1} \times G_{y}^{k-1} \times G_{z}^{k-1}$,
-where $G_{x}^{k-1}$ is obtained by deleting every other grid
-point of $G_x^k$ and similarly for $G_{y}^k$ and $G_{z}^k$.
-\end{lemma}
-
-To our knowledge, the m-tree previously has not been applied in this
-fashion to the numerical factorization, but it has been used,
-directly or indirectly, in several optimal order algorithms for
-computing the fill-in during the symbolic factorization phase
-[4] - [10], [5], [6]. In \S 1.3., we analyze the complexity of the old and new
-approaches to the intersection problem for the special case of
-an $n \times n$ grid ordered by nested dissection. The special
-structure of this problem allows us to make exact estimates of
-the complexity. To our knowledge, the m-tree previously has not been applied in this
-fashion to the numerical factorization, but it has been used,
-directly or indirectly, in several optimal order algorithms for
-computing the fill-in during the symbolic factorization phase
-[4] - [10], [5], [6].
-
-In \S 1.2, we review the bordering algorithm, and introduce
-the sorting and intersection problems that arise in the
-sparse formulation of the algorithm.
-In \S 1.3., we analyze the complexity of the old and new
-approaches to the intersection problem for the special case of
-an $n \times n$ grid ordered by nested dissection. The special
-structure of this problem allows us to make exact estimates of
-the complexity. To our knowledge, the m-tree previously has not been applied in this
-fashion to the numerical factorization, but it has been used,
-directly or indirectly, in several optimal order algorithms for
-computing the fill-in during the symbolic factorization phase
-[4] - [10], [5], [6].
-
-
-For the old approach, we show that the
-complexity of the intersection problem is $O(n^{3})$, the same
-as the complexity of the numerical computations. For the
-new approach, the complexity of the second part is reduced to
-$O(n^{2} (\log n)^{2})$.
-
-To our knowledge, the m-tree previously has not been applied in this
-fashion to the numerical factorization, but it has been used,
-directly or indirectly, in several optimal order algorithms for
-computing the fill-in during the symbolic factorization phase
-[4] - [10], [5], [6]. In \S 1.3., we analyze the complexity of the old and new
-approaches to the intersection problem for the special case of
-an $n \times n$ grid ordered by nested dissection. The special
-structure of this problem allows us to make exact estimates of
-the complexity. To our knowledge, the m-tree previously has not been applied in this
-fashion to the numerical factorization, but it has been used,
-directly or indirectly, in several optimal order algorithms for
-computing the fill-in during the symbolic factorization phase
-[4] - [10], [5], [6].
-This is accomplished by exploiting the m-tree,
-a particular spanning tree for the graph of the filled-in matrix.
-To our knowledge, the m-tree previously has not been applied in this
-fashion to the numerical factorization, but it has been used,
-directly or indirectly, in several optimal order algorithms for
-computing the fill-in during the symbolic factorization phase
-\cite{EISENSTAT} - \cite{LIU2}, \cite{ROSE76}, \cite{SCHREIBER}.
-
-\subsection{Robustness.}\ We do not
-attempt to present an overview
-here, but rather attempt to focus on those results that
-are relevant to our particular algorithm.
-This section assumes prior knowledge of the role of graph theory
-in sparse Gaussian elimination; surveys of this role are
-available in \cite{ROSE72} and \cite{GEORGELIU}. More general
-discussions of elimination trees are given in
-\cite{LAW} - \cite{LIU2}, \cite{SCHREIBER}.
-Thus, at the $k$th stage, the bordering algorithm consists of
-solving the lower triangular system
-\begin{equation} \label{1.2}
- L_{k-1}v = c
-\end{equation}
-and setting
-\begin{eqnarray}
-\ell &=& D^{-1}_{k-1}v , \\
-\delta &=& \alpha - \ell^{t} v .
-\end{eqnarray}
-
-\begin{figure}
-\vspace{14pc}
-\caption{This is a figure 1.1.}
-\end{figure}
-
-\section{Robustness.} We do not
-attempt to present an overview
-here, but rather attempt to focus on those results that
-are relevant to our particular algorithm.
-
-\subsection{Versatility.}\ The special
-structure of this problem allows us to make exact estimates of
-the complexity. For the old approach, we show that the
-complexity of the intersection problem is $O(n^{3})$, the same
-as the complexity of the numerical computations
-\cite{GEORGELIU}, \cite{ROSEWHITTEN}. For the
-new approach, the complexity of the second part is reduced to
-$O(n^{2} (\log n)^{2})$.
-
-To our knowledge, the m-tree previously has not been applied in this
-fashion to the numerical factorization, but it has been used,
-directly or indirectly, in several optimal order algorithms for
-computing the fill-in during the symbolic factorization phase
-[4] - [10], [5], [6]. In \S 1.3., we analyze the complexity of the old and new
-approaches to the intersection problem for the special case of
-an $n \times n$ grid ordered by nested dissection. The special
-structure of this problem allows us to make exact estimates of
-the complexity. To our knowledge, the m-tree previously has not been applied in this
-fashion to the numerical factorization, but it has been used,
-directly or indirectly, in several optimal order algorithms for
-computing the fill-in during the symbolic factorization phase
-[4] - [10], [5], [6].
-
-In \S 1.2, we review the bordering algorithm, and introduce
-the sorting and intersection problems that arise in the
-sparse formulation of the algorithm.
-In \S 1.3., we analyze the complexity of the old and new
-approaches to the intersection problem for the special case of
-an $n \times n$ grid ordered by nested dissection. The special
-structure of this problem allows us to make exact estimates of
-the complexity. To our knowledge, the m-tree previously has not been applied in this
-fashion to the numerical factorization, but it has been used,
-directly or indirectly, in several optimal order algorithms for
-computing the fill-in during the symbolic factorization phase
-[4] - [10], [5], [6].
-
-
-For the old approach, we show that the
-complexity of the intersection problem is $O(n^{3})$, the same
-as the complexity of the numerical computations. For the
-new approach, the complexity of the second part is reduced to
-$O(n^{2} (\log n)^{2})$.
-
-To our knowledge, the m-tree previously has not been applied in this
-fashion to the numerical factorization, but it has been used,
-directly or indirectly, in several optimal order algorithms for
-computing the fill-in during the symbolic factorization phase
-[4] - [10], [5], [6]. In \S 1.3., we analyze the complexity of the old and new
-approaches to the intersection problem for the special case of
-an $n \times n$ grid ordered by nested dissection. The special
-structure of this problem allows us to make exact estimates of
-the complexity. To our knowledge, the m-tree previously has not been applied in this
-fashion to the numerical factorization, but it has been used,
-directly or indirectly, in several optimal order algorithms for
-computing the fill-in during the symbolic factorization phase
-[4] - [10], [5], [6].
-This is accomplished by exploiting the m-tree,
-a particular spanning tree for the graph of the filled-in matrix.
-To our knowledge, the m-tree previously has not been applied in this
-fashion to the numerical factorization, but it has been used,
-directly or indirectly, in several optimal order algorithms for
-computing the fill-in during the symbolic factorization phase
-\cite{EISENSTAT} - \cite{LIU2}, \cite{ROSE76}, \cite{SCHREIBER}.
-
-\begin{thebibliography}{99}
-
-%\bibitem{GUIDE}
-%R.~E. Bank, {\em PLTMG users' guide, edition 5.0}, tech. report,
-% Department of Mathematics, University of California, San Diego, CA, 1988.
-
-%\bibitem{HBMG}
-%R.~E. Bank, T.~F. Dupont, and H.~Yserentant, {\em The hierarchical basis
-% multigrid method}, Numer. Math., 52 (1988), pp.~427--458.
-
-\bibitem{BANKSMITH}
-R.~E. Bank and R.~K. Smith, {\em General sparse elimination requires no
- permanent integer storage}, SIAM J. Sci. Stat. Comput., 8 (1987),
- pp.~574--584.
-
-\bibitem{EISENSTAT}
-S.~C. Eisenstat, M.~C. Gursky, M.~Schultz, and A.~Sherman, {\em
- Algorithms and data structures for sparse symmetric gaussian elimination},
- SIAM J. Sci. Stat. Comput., 2 (1982), pp.~225--237.
-
-\bibitem{GEORGELIU}
-A.~George and J.~Liu, {\em Computer Solution of Large Sparse Positive
- Definite Systems}, Prentice Hall, Englewood Cliffs, NJ, 1981.
-
-\bibitem{LAW}
-K.~H. Law and S.~J. Fenves, {\em A node addition model for symbolic
- factorization}, ACM TOMS, 12 (1986), pp.~37--50.
-
-\bibitem{LIU}
-J.~W.~H. Liu, {\em A compact row storage scheme for cholesky factors
- using elimination trees}, ACM TOMS, 12 (1986), pp.~127--148.
-
-\bibitem{LIU2}
-\sameauthor , {\em The role of
- elimination trees in sparse factorization}, Tech. Report CS-87-12,Department
- of Computer Science, York University, Ontario, Canada, 1987.
-
-\bibitem{ROSE72}
-D.~J. Rose, {\em A graph theoretic study of the numeric solution of
- sparse positive definite systems}, in Graph Theory and Computing, Academic Press, New
-York, 1972.
-
-\bibitem{ROSE76}
-D.~J. Rose, R.~E. Tarjan, and G.~S. Lueker, {\em Algorithmic aspects of
- vertex elimination on graphs}, SIAM J. Comput., 5 (1976), pp.~226--283.
-
-\bibitem{ROSEWHITTEN}
-D.~J. Rose and G.~F. Whitten, {\em A recursive analysis of disection
- strategies}, in Sparse Matrix Computations, Academic Press, New York, 1976.
-
-\bibitem{SCHREIBER}
-R.~Schrieber, {\em A new implementation of sparse gaussian elimination},
- ACM TOMS, 8 (1982), pp.~256--276.
-
-\end{thebibliography}
-\end{document}
-
-% End of ltexpprt.tex
-%
-
-
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% ltexpprt.sty %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%
-% This is ltexpprt.sty, a file of macros and definitions for creating a
-% chapter for publication in the ACM/SIAM Preprint series using LaTeX2E.
-% It is designed to produce double-column output.
-% This file may be freely distributed but may not be altered in any way.
-% Any comments or questions regarding these macros should be directed to:
-
-% Corey Gray
-% SIAM
-% 3600 University City Science Center
-% Philadelphia, PA 19104-2688
-% USA
-% Telephone: (215) 382-9800
-% Fax: (215) 386-7999
-% e-mail: gray@siam.org
-
-
-% Report the version.
-\message{*** ACM/SIAM LaTeX2E Preprint Series macro package, version 1.0,
-September 5, 1996 ***}
-
-
-\pretolerance=800
-\tolerance=10000
-\sloppy
-
-%\voffset=-.5in
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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@
- \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 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%
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-% 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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