X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/Krylov_multi.git/blobdiff_plain/85655e85f4c16a68071ffbf5ab526639839a4a72..c0329df983b381995f844afef4536e2853e59e78:/krylov_multi.tex?ds=sidebyside

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-alalal
+\documentclass{article}
+\usepackage[utf8]{inputenc}
+\usepackage{amsfonts,amssymb}
+\usepackage{amsmath}
+\usepackage{graphicx}
+
+\title{A scalable multisplitting algorithm for solving large sparse linear systems} 
+
+
+
+\begin{document}
+\author{Raphaël Couturier \and Lilia Ziane Khodja}
+
+\maketitle
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%
+%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+\begin{abstract}
+In  this  paper we  revist  the  krylov  multisplitting algorithm  presented  in
+\cite{huang1993krylov}  which  uses  a  scalar  method to  minimize  the  krylov
+iterations computed by a multisplitting algorithm. Our new algorithm is simply a
+parallel multisplitting algorithm  with few blocks of large  size and a parallel
+krylov  minimization  is used  to  improve  the  convergence. Some  large  scale
+experiments  with a 3D  Poisson problem  are presented.  They show  the obtained
+improvements compared to a classical GMRES both in terms of number of iterations
+and execution times.
+\end{abstract}
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%
+%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+\section{Introduction}
+
+Iterative methods are used to solve  large sparse linear systems of equations of
+the form  $Ax=b$ because they are  easier to parallelize than  direct ones. Many
+iterative  methods have  been proposed  and adpated  by many  researchers.  When
+solving large  linear systems  with many cores,  iterative methods  often suffer
+from  scalability  problems.    This  is  due  to  their   need  for  collective
+communications to perform matrix-vector products and reduction operations.
+
+%%%%% Lilia
+% doit-on définir le principe et les préliminaires du multisplitting dans l'intro ou dans l'autre section? 
+% valides-tu le titre de la 2eme section? celle que je voudrai rédiger.
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%
+%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+\section{A two-stage method with a minimization}
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%
+%%%%%%%%%%%%%%%%%%%%%%%%
+
+\bibliographystyle{plain}
+\bibliography{biblio}
+
+\end{document}