X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/GMRES2stage.git/blobdiff_plain/928901c5a41a83e85eff69fe0869d4653bf1079e..a77eb57aac4b8cfd03ac650c5a61167f8647e458:/paper.tex

diff --git a/paper.tex b/paper.tex
index 709ae37..0c0299f 100644
--- a/paper.tex
+++ b/paper.tex
@@ -431,7 +431,7 @@ Email: lilia.ziane@inria.fr}
 \end{abstract}
 
 \begin{IEEEkeywords}
-Iterative Krylov methods; sparse linear systems; error minimization; PETSC; %à voir... 
+Iterative Krylov methods; sparse linear systems; error minimization; PETSc; %à voir... 
 \end{IEEEkeywords}
 
 
@@ -546,7 +546,7 @@ However, the iterative methods suffer from scalability problems on parallel comp
 
 In this paper we propose a two-stage algorithm based on two nested iterations called inner-outer iterations. The algorithm consists in solving the sparse linear system iteratively with a small number of inner iterations and restarts the outer step with a new solution minimizing some error function over a Krylov subspace. The algorithm is iterative and easy to parallelize on large clusters and the minimization technique improves its convergence and performances.
 
-The present paper is organized as follows. In Section~\ref{sec:02} some related works are presented. Section~\ref{sec:03} presents our two-stage algorithm based on Krylov subspace iteration methods. Section~\ref{sec:04} shows some experimental results obtained on large clusters of our algorithm using routines of PETSc toolkit.    
+The present paper is organized as follows. In Section~\ref{sec:02} some related works are presented. Section~\ref{sec:03} presents our two-stage algorithm based on Krylov subspace iteration methods. Section~\ref{sec:04} shows some experimental results obtained on large clusters of our algorithm using routines of PETSc toolkit.  
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