X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/Krylov_multi.git/blobdiff_plain/fedf59562159b08c86b61f27de746deb1fd42f98..c0329df983b381995f844afef4536e2853e59e78:/krylov_multi.tex?ds=sidebyside

diff --git a/krylov_multi.tex b/krylov_multi.tex
index 5cf4056..b96a5b9 100644
--- a/krylov_multi.tex
+++ b/krylov_multi.tex
@@ -14,19 +14,51 @@
 \maketitle
 
 
+%%%%%%%%%%%%%%%%%%%%%%%%
+%%%%%%%%%%%%%%%%%%%%%%%%
+
+
 \begin{abstract}
-In this paper  we revist the krylov multisplitting  algorithm presented in [ref]
-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.
+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 used  to solve large sparse linear systems  of the form $Ax=b$
-because they are easier to parallelize than direct ones.
+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}