\maketitle
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+%%%%%%%%%%%%%%%%%%%%%%%%
+
+
\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}
+
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+%%%%%%%%%%%%%%%%%%%%%%%%
+
+
\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.
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%
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+
+
+\section{A two-stage method with a minimization}
+
+
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+
+\bibliographystyle{plain}
+\bibliography{biblio}
\end{document}
