From 5e3a7342021a720e17be4f147b4e73e5ad5396b9 Mon Sep 17 00:00:00 2001 From: couturie Date: Wed, 8 Jan 2014 18:25:22 +0100 Subject: [PATCH 1/1] new --- biblio.bib | 9 ++++++++- krylov_multi.tex | 11 ++++++++--- 2 files changed, 16 insertions(+), 4 deletions(-) diff --git a/biblio.bib b/biblio.bib index 55c4a93..e45f5d6 100644 --- a/biblio.bib +++ b/biblio.bib @@ -77,7 +77,14 @@ @TechReport{prace-multi, author = {Nick Brown and J. Mark Bull and Iain Bethune}, title = {Solving Large Sparse Linear Systems using Asynchronous Multisplitting}, - institution = {PRACE White paper n°WP84}, + institution = {PRACE White paper number WP84}, year = {2013}, } +@Book{S96, + author = {Y. Saad}, + title = {Iterative Methods for Sparse Linear Systems}, + publisher = {PWS Publishing}, + year = {1996}, + address = {New York}, +} diff --git a/krylov_multi.tex b/krylov_multi.tex index 40380d0..91e4745 100644 --- a/krylov_multi.tex +++ b/krylov_multi.tex @@ -38,9 +38,14 @@ classical GMRES both in terms of number of iterations and execution times. Iterative methods are used to solve large sparse linear systems of equations of the form $Ax=b$ because they are easier to parallelize than direct ones. Many -iterative methods have been proposed and adapted by many researchers. When -solving large linear systems with many cores, iterative methods often suffer -from scalability problems. This is due to their need for collective +iterative methods have been proposed and adapted by many researchers. For +example, the GMRES method and the Conjugate Gradient method are very well known +and used by many researchers ~\cite{S96}. Both the method are based on the +Krylov subspace which consists in forming a basis of the sequence of successive +matrix powers times the initial residual. + +When solving large linear systems with many cores, iterative methods often +suffer from scalability problems. This is due to their need for collective communications to perform matrix-vector products and reduction operations. Preconditionners can be used in order to increase the convergence of iterative solvers. However, most of the good preconditionners are not sclalable when -- 2.39.5