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.
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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
