11-12-2014 v05

[Krylov_multi.git] / krylov_multi.tex

diff --git a/krylov_multi.tex b/krylov_multi.tex
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--- a/krylov_multi.tex
+++ b/krylov_multi.tex
@@ -94,8 +94,6 @@ method. In opposition to traditional multisplitting method that suffer from slow
 convergence, as  proposed in~\cite{huang1993krylov},  the use of  a minimization
 process can drastically improve the convergence.
 
 convergence, as  proposed in~\cite{huang1993krylov},  the use of  a minimization
 process can drastically improve the convergence.
 

-In this work we develop a new parallel two-stage algorithm for large-scale clusters. Our objective is to mix between Krylov based iterative methods and the multisplitting method to improve the scalability. In fact Krylov subspace methods are well-known for their good convergence compared to others iterative methods. So our main contribution is to use the multisplitting method which splits the problem to solve into different sub-problems in order to reduce the large amount of communications and, to implement both inner and outer iterations as Krylov subspace iterations improving the convergence of the multisplitting algorithm.
-

 The present paper is  organized as follows. First, Section~\ref{sec:02} presents
 some  related  works and  the  principle  of  multisplitting methods.  Then,  in
 Section~\ref{sec:03}  the algorithm  of our  Krylov multisplitting
 The present paper is  organized as follows. First, Section~\ref{sec:02} presents
 some  related  works and  the  principle  of  multisplitting methods.  Then,  in
 Section~\ref{sec:03}  the algorithm  of our  Krylov multisplitting