X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/GMRES2stage.git/blobdiff_plain/e31850a4ae1376cd865f5e3fb950c9bbd3bdeeb8..70ad0cb4dcbf00dcc4bade65051bf0273854d231:/paper.tex

diff --git a/paper.tex b/paper.tex
index b755e4c..51eab5c 100644
--- a/paper.tex
+++ b/paper.tex
@@ -367,7 +367,7 @@
 %
 % paper title
 % can use linebreaks \\ within to get better formatting as desired
-\title{A Krylov two-stage algorithm to solve large sparse linear systems}
+\title{TSARM: A Two-Stage Algorithm with least-square Residual Minimization to solve large sparse linear systems}
 %où
 %\title{A two-stage algorithm with error minimization to solve large sparse linear systems}
 %où
@@ -423,7 +423,16 @@ Email: lilia.ziane@inria.fr}
 
 
 \begin{abstract}
-%The abstract goes here. DO NOT USE SPECIAL CHARACTERS, SYMBOLS, OR MATH IN YOUR TITLE OR ABSTRACT.
+In  this paper  we propose  a  two stage  iterative method  which increases  the
+convergence of Krylov iterative methods,  typically those of GMRES variants. The
+principle of  our approach  is to  build an external  iteration over  the Krylov
+method  and to  save  the current  residual  frequently (for  example, for  each
+restart of GMRES). Then after a given number of outer iterations, a minimization
+step is applied on the matrix composed of the save residuals in order to compute
+a  better solution and  make a  new iteration  if necessary.  We prove  that our
+method  has the  same  convergence property  than  the inner  method used.  Some
+experiments using up  to 16,394 cores show that compared  to GMRES our algorithm
+can be around 7 times faster.
 \end{abstract}
 
 \begin{IEEEkeywords}
@@ -777,6 +786,11 @@ Larger experiments ....
 %%%*********************************************************
 
 
+future plan : \\
+- study other kinds of matrices, problems, inner solvers\\
+- adaptative number of outer iterations to minimize\\
+- implement our solver inside PETSc
+
 
 % conference papers do not normally have an appendix