X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/GMRES2stage.git/blobdiff_plain/776dc9de2f52ea929d89b8322268b6abf2098b45..1082caa290770800e8a7f6815ed153931cd93460:/paper.tex

diff --git a/paper.tex b/paper.tex
index c60a306..185bbf3 100644
--- a/paper.tex
+++ b/paper.tex
@@ -348,28 +348,45 @@
 \hyphenation{op-tical net-works semi-conduc-tor}
 
 
+
+\usepackage{algorithm}
+\usepackage{algpseudocode}
+
+\algnewcommand\algorithmicinput{\textbf{Input:}}
+\algnewcommand\Input{\item[\algorithmicinput]}
+
+\algnewcommand\algorithmicoutput{\textbf{Output:}}
+\algnewcommand\Output{\item[\algorithmicoutput]}
+
+
+
 \begin{document}
 %
 % paper title
 % can use linebreaks \\ within to get better formatting as desired
-\title{Bare Demo of IEEEtran.cls for IEEECS Conferences}
+\title{A Krylov two-stage algorithm to solve large sparse linear systems}
+%où
+%\title{A two-stage algorithm with error minimization to solve large sparse linear systems}
+%où
+%\title{???}
 
 
 % author names and affiliations
 % use a multiple column layout for up to two different
 % affiliations
 
-\author{\IEEEauthorblockN{Authors Name/s per 1st Affiliation (Author)}
-\IEEEauthorblockA{line 1 (of Affiliation): dept. name of organization\\
-line 2: name of organization, acronyms acceptable\\
-line 3: City, Country\\
-line 4: Email: name@xyz.com}
+\author{\IEEEauthorblockN{Rapha\"el Couturier}
+\IEEEauthorblockA{Femto-ST Institute - DISC Department\\
+Universit\'e de Franche-Comt\'e, IUT de Belfort-Montb\'eliard\\
+19 avenue de Mar\'echal Juin, BP 527 \\
+90016 Belfort Cedex, France\\
+Email: raphael.couturier@univ-fcomte.fr}
 \and
-\IEEEauthorblockN{Authors Name/s per 2nd Affiliation (Author)}
-\IEEEauthorblockA{line 1 (of Affiliation): dept. name of organization\\
-line 2: name of organization, acronyms acceptable\\
-line 3: City, Country\\
-line 4: Email: name@xyz.com}
+\IEEEauthorblockN{Lilia Ziane Khodja}
+\IEEEauthorblockA{Centre de Recherche INRIA Bordeaux Sud-Ouest\\
+200 avenue de la Vieille Tour\\
+33405 Talence Cedex, France\\
+Email: lilia.ziane@inria.fr}
 }
 
 % conference papers do not typically use \thanks and this command
@@ -408,13 +425,11 @@ line 4: Email: name@xyz.com}
 
 
 \begin{abstract}
-The abstract goes here. DO NOT USE SPECIAL CHARACTERS, SYMBOLS, OR MATH IN YOUR TITLE OR ABSTRACT.
-
+%The abstract goes here. DO NOT USE SPECIAL CHARACTERS, SYMBOLS, OR MATH IN YOUR TITLE OR ABSTRACT.
 \end{abstract}
 
 \begin{IEEEkeywords}
-component; formatting; style; styling;
-
+Iterative Krylov methods; sparse linear systems; error minimization; PETSC; %à voir... 
 \end{IEEEkeywords}
 
 
@@ -430,26 +445,6 @@ component; formatting; style; styling;
 
 
 
-\section{Introduction}
-% no \IEEEPARstart
-This demo file is intended to serve as a ``starter file''
-for IEEE conference papers produced under \LaTeX\ using
-IEEEtran.cls version 1.7 and later.
-
-All manuscripts must be in English. These guidelines include complete descriptions of the fonts, spacing, and related information for producing your proceedings manuscripts. Please follow them and if you have any questions, direct them to the production editor in charge of your proceedings at Conference Publishing Services (CPS): Phone +1 (714) 821-8380 or Fax +1 (714) 761-1784.
-% You must have at least 2 lines in the paragraph with the drop letter
-% (should never be an issue)
-
-\subsection{Subsection Heading Here}
-Subsection text here.
-
-
-\subsubsection{Subsubsection Heading Here}
-Subsubsection text here.
-
-\section{Type style and Fonts}
-Wherever Times is specified, Times Roman or Times New Roman may be used. If neither is available on your system, please use the font closest in appearance to Times. Avoid using bit-mapped fonts if possible. True-Type 1 or Open Type fonts are preferred. Please embed symbol fonts, as well, for math, etc.
-
 
 % An example of a floating figure using the graphicx package.
 % Note that \label must occur AFTER (or within) \caption.
@@ -535,18 +530,85 @@ Wherever Times is specified, Times Roman or Times New Roman may be used. If neit
 
 
 
+%%%*********************************************************
+%%%*********************************************************
+\section{Introduction}
+% no \IEEEPARstart
+% You must have at least 2 lines in the paragraph with the drop letter
+% (should never be an issue)
+%%%*********************************************************
+%%%*********************************************************
+
+
+
+%%%*********************************************************
+%%%*********************************************************
+\section{Related works}
+%Wherever Times is specified, Times Roman or Times New Roman may be used. If neither is available on your system, please use the font closest in appearance to Times. Avoid using bit-mapped fonts if possible. True-Type 1 or Open Type fonts are preferred. Please embed symbol fonts, as well, for math, etc.
+%%%*********************************************************
+%%%*********************************************************
+
+
+
+%%%*********************************************************
+%%%*********************************************************
+\section{A Krylov two-stage algorithm}
+We propose a two-stage algorithm to solve large sparse linear systems of the form $Ax=b$ based on iterative Krylov sub-space methods.
+
+
+\begin{algorithm}[!h]
+\caption{A Krylov two-stage algorithm}
+\begin{algorithmic}[1]
+  \Input $A$ (sparse matrix), $b$ (right-hand side)
+  \Output $x$ (solution vector)\vspace{0.2cm}
+  \State Set the initial guess $x^0$
+  \For {$k=1,2,3,\ldots$ until convergence}
+    \State Solve iteratively $Ax^k=b$
+    \State Add vector $x^k$ to Krylov basis $S$
+    \If {$k$ mod $s=0$ {\bf and} not convergence}
+      \State Compute dense matrix $R=AS$
+      \State Solve least-squares problem $\|b-R\alpha\|_2$
+      \State Compute minimizer $x^k=S\alpha$
+      \State Reinitialize Krylov basis $S$
+    \EndIf
+  \EndFor
+\end{algorithmic}
+\label{algo:01}
+\end{algorithm}
+%%%*********************************************************
+%%%*********************************************************
+
+
+
+%%%*********************************************************
+%%%*********************************************************
+\section{Experiments using petsc}
+%%%*********************************************************
+%%%*********************************************************
+
+
+
+%%%*********************************************************
+%%%*********************************************************
 \section{Conclusion}
-The conclusion goes here. this is more of the conclusion
+%The conclusion goes here. this is more of the conclusion
+%%%*********************************************************
+%%%*********************************************************
+
+
 
 % conference papers do not normally have an appendix
 
 
+
 % use section* for acknowledgement
+%%%*********************************************************
+%%%*********************************************************
 \section*{Acknowledgment}
-
-
-The authors would like to thank...
-more thanks here
+%The authors would like to thank...
+%more thanks here
+%%%*********************************************************
+%%%*********************************************************
 
 
 % trigger a \newpage just before the given reference
@@ -574,8 +636,8 @@ more thanks here
 \begin{thebibliography}{1}
 
 \bibitem{IEEEhowto:kopka}
-H.~Kopka and P.~W. Daly, \emph{A Guide to \LaTeX}, 3rd~ed.\hskip 1em plus
-  0.5em minus 0.4em\relax Harlow, England: Addison-Wesley, 1999.
+%H.~Kopka and P.~W. Daly, \emph{A Guide to \LaTeX}, 3rd~ed.\hskip 1em plus
+%  0.5em minus 0.4em\relax Harlow, England: Addison-Wesley, 1999.
 
 \end{thebibliography}