From: raphael couturier Date: Sun, 5 Oct 2014 19:10:03 +0000 (+0200) Subject: abstract à relire X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/GMRES2stage.git/commitdiff_plain/70ad0cb4dcbf00dcc4bade65051bf0273854d231?ds=inline abstract à relire --- 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