From 0152824d3e001a7084c17325a1171e9efe4c51ec Mon Sep 17 00:00:00 2001 From: raphael couturier Date: Fri, 10 Oct 2014 11:31:47 +0200 Subject: [PATCH] new --- paper.tex | 21 +++++++++++---------- 1 file changed, 11 insertions(+), 10 deletions(-) diff --git a/paper.tex b/paper.tex index e3d19ec..fe7fa39 100644 --- a/paper.tex +++ b/paper.tex @@ -425,16 +425,17 @@ Email: lilia.ziane@inria.fr} \begin{abstract} -In this article, a two-stage iterative algorithm is proposed to improve the -convergence of Krylov based iterative methods, typically those of GMRES variants. The -principle of the proposed approach is to build an external iteration over the Krylov -method, and to frequently store its current residual (at each -GMRES restart for instance). After a given number of outer iterations, a minimization -step is applied on the matrix composed by the saved residuals, in order to -compute a better solution and to make new iterations if required. It is proven that -the proposal has the same convergence properties than the inner embedded method itself. -Experiments using up to 16,394 cores also show that the proposed algorithm -runs around 5 or 7 times faster than GMRES. +In this article, a two-stage iterative algorithm is proposed to improve the +convergence of Krylov based iterative methods, typically those of GMRES +variants. The principle of the proposed approach is to build an external +iteration over the Krylov method, and to frequently store its current residual +(at each GMRES restart for instance). After a given number of outer iterations, +a least-squares minimization step is applied on the matrix composed by the saved +residuals, in order to compute a better solution and to make new iterations if +required. It is proven that the proposal has the same convergence properties +than the inner embedded method itself. Experiments using up to 16,394 cores +also show that the proposed algorithm runs around 5 or 7 times faster than +GMRES. \end{abstract} \begin{IEEEkeywords} -- 2.39.5