deletions | additions       diff --git a/ex_shared.tex b/ex_shared.tex  new file mode 100644  index 0000000..2906cd6  --- /dev/null  +++ b/ex_shared.tex 
...
% SIAM Shared Information Template  % This is information that is shared between the main document and any  % supplement. If no supplement is required, then this information can  % be included directly in the main document.  % Packages and macros go here  \usepackage{lipsum}  \usepackage{amsfonts}  \usepackage{graphicx}  \usepackage{epstopdf}  \usepackage{algorithmic}  \ifpdf  \DeclareGraphicsExtensions{.eps,.pdf,.png,.jpg}  \else  \DeclareGraphicsExtensions{.eps}  \fi  % Declare title and authors, without \thanks  \newcommand{\TheTitle}{\include{title}}  \newcommand{\TheAuthors}{J. Chen and A. S. Edelman}  % Sets running headers as well as PDF title and authors  \headers{\TheTitle}{\TheAuthors}  % Title. If the supplement option is on, then "Supplementary Material"  % is automatically inserted before the title.  \title{{\TheTitle}\thanks{This work was funded by the Fog Research Institute under contract no.~FRI-454.}}  % Authors: full names plus addresses.  \author{  Jiahao Chen  \and  Alan S. Edelman\thanks{Department of Mathematics, and The Computer Science And Artificial Intelligence Laboratory, Massachusetts Institute of Technology, Cambridge, MA  (\email{\{jiahao,edelman\}@mit.edu})},  }  \usepackage{amsopn}  \DeclareMathOperator{\diag}{diag}  %%% Local Variables:  %%% mode:latex  %%% TeX-master: "ex_article"  %%% End:  diff --git a/main.tex b/main.tex  index 6e39ebe..532782d 100644  --- a/main.tex  +++ b/main.tex 
...
68Q25, 68R10, 68U05  \end{AMS}  \section{Introduction}  The introduction introduces the context and summarizes the  manuscript. It is importantly to clearly state the contributions of  this piece of work. The next two paragraphs are text filler,  generated by the \texttt{lipsum} package.  \lipsum[2-3]  % The outline is not required, but we show an example here.  The paper is organized as follows. Our main results are in  \cref{sec:main}, our new algorithm is in \cref{sec:alg}, experimental  results are in \cref{sec:experiments}, and the conclusions follow in  \cref{sec:conclusions}.  \section{Main results}  \label{sec:main}  We interleave text filler with some example theorems and theorem-like  items.  \lipsum[4]  Here we state our main result as \cref{thm:bigthm}; the proof is  deferred to \cref{sec:proof}.  \begin{theorem}[$LDL^T$ Factorization \cite{GoVa13}]\label{thm:bigthm}  If $A \in \mathbb{R}^{n \times n}$ is symmetric and the principal  submatrix $A(1:k,1:k)$ is nonsingular for $k=1:n-1$, then there  exists a unit lower triangular matrix $L$ and a diagonal matrix  \begin{displaymath}  D = \diag(d_1,\dots,d_n)  \end{displaymath}  such that $A=LDL^T$. The factorization is unique.  \end{theorem}  \lipsum[6]  \begin{theorem}[Mean Value Theorem]\label{thm:mvt}  Suppose $f$ is a function that is continuous on the closed interval  $[a,b]$. and differentiable on the open interval $(a,b)$.  Then there exists a number $c$ such that $a < c < b$ and  \begin{displaymath}  f'(c) = \frac{f(b)-f(a)}{b-a}.  \end{displaymath}  In other words,  \begin{displaymath}  f(b)-f(a) = f'(c)(b-a).  \end{displaymath}  \end{theorem}  Observe that \cref{thm:bigthm,thm:mvt,cor:a} correctly mix references  to multiple labels.  \begin{corollary}\label{cor:a}  Let $f(x)$ be continuous and differentiable everywhere. If $f(x)$  has at least two roots, then $f'(x)$ must have at least one root.  \end{corollary}  \begin{proof}  Let $a$ and $b$ be two distinct roots of $f$.  By \cref{thm:mvt}, there exists a number $c$ such that  \begin{displaymath}  f'(c) = \frac{f(b)-f(a)}{b-a} = \frac{0-0}{b-a} = 0.  \end{displaymath}  \end{proof}  Note that it may require two \LaTeX\ compilations for the proof marks  to show.  Display matrices can be rendered using environments from \texttt{amsmath}:  \begin{equation}\label{eq:matrices}  S=\begin{bmatrix}1&0\\0&0\end{bmatrix}  \quad\text{and}\quad  C=\begin{pmatrix}1&1&0\\1&1&0\\0&0&0\end{pmatrix}.  \end{equation}  Equation \cref{eq:matrices} shows some example matrices.  We calculate the Fr\'{e}chet derivative of $F$ as follows:  \begin{subequations}  \begin{align}  F'(U,V)(H,K)  &= \langle R(U,V),H\Sigma V^{T} + U\Sigma K^{T} -  P(H\Sigma V^{T} + U\Sigma K^{T})\rangle \label{eq:aa} \\  &= \langle R(U,V),H\Sigma V^{T} + U\Sigma K^{T}\rangle  \nonumber \\  &= \langle R(U,V)V\Sigma^{T},H\rangle +  \langle \Sigma^{T}U^{T}R(U,V),K^{T}\rangle. \label{eq:bb}  \end{align}  \end{subequations}  \Cref{eq:aa} is the first line, and \cref{eq:bb} is the last line.  \section{Algorithm}  \label{sec:alg}  \lipsum[40]  Our analysis leads to the algorithm in \cref{alg:buildtree}.  \begin{algorithm}  \caption{Build tree}  \label{alg:buildtree}  \begin{algorithmic}  \STATE{Define $P:=T:=\{ \{1\},\ldots,\{d\}$\}}  \WHILE{$\#P > 1$}  \STATE{Choose $C^\prime\in\mathcal{C}_p(P)$ with $C^\prime := \operatorname{argmin}_{C\in\mathcal{C}_p(P)} \varrho(C)$}  \STATE{Find an optimal partition tree $T_{C^\prime}$ }  \STATE{Update $P := (P{\setminus} C^\prime) \cup \{ \bigcup_{t\in C^\prime} t \}$}  \STATE{Update $T := T \cup \{ \bigcup_{t\in\tau} t : \tau\in T_{C^\prime}{\setminus} \mathcal{L}(T_{C^\prime})\}$}  \ENDWHILE  \RETURN $T$  \end{algorithmic}  \end{algorithm}  \lipsum[41]  \section{Experimental results}  \label{sec:experiments}  \lipsum[50]  \Cref{fig:testfig} shows some example results. Additional results are  available in the supplement in \cref{tab:foo}.  \begin{figure}[htbp]  \centering  \label{fig:a}\includegraphics{lexample_fig1}  \caption{Example figure using external image files.}  \label{fig:testfig}  \end{figure}  \lipsum[51]  \section{Discussion of \texorpdfstring{{\boldmath$Z=X \cup Y$}}{Z = X union Y}}  \lipsum[76]  \section{Conclusions}  \label{sec:conclusions}  Some conclusions here.  \appendix  \section{An example appendix}  \lipsum[71] \include{include}  \section*{Acknowledgments}  Julia is an open source programming language freely available from \href{http://julialang.org}.  We would like thank the many Julia users and developers who have contributed  toacknowledge  the assistance lively  discussion  of volunteers in putting  together this example manuscript GitHub issue  \href{https://github.com/JuliaLang/julia/issues/4774}{JuliaLang/julia/4774},  especially Jeff Bezanson, Simon Byrne, Jutho Haegeman, Stefan Karpinski,  and supplement. Matthew Bauman.  \bibliographystyle{siamplain}  \bibliography{bibliography/biblio}