Rational approximation preconditioners for sparse linear systems.
type: Item
instance of: scholarly article
title: Rational approximation preconditioners for sparse linear systems.
zbMATH Open document ID: 1033.65029
DOI: 10.1016/S0377-0427(03)00480-1
author: P. Guillaume
author: Y. Saad
author: Masha Sosonkina
published in: Journal of Computational and Applied Mathematics
publication date: 2003-10-15T00:00:00Z
review text: This paper deals with incomplete LU factorization preconditioners of very ill-conditioned matrices. A class of preconditioning techniques is presented. The idea is exploiting a rational approximation to the inverse of the shifted original matrix and then an incomplete LU factorization of the resulting matrix is computed. The resulting factors are then used to compute a better preconditioner for the original matrix. As a good LU factorization can be obtained without allowing much fill-in, the main motivation for this process is to save memory. A theoretical analysis and numerical experiments are presented to show that the resulting method can succeed in solving rather difficult problems.
Mathematics Subject Classification ID: 65F35
Mathematics Subject Classification ID: 65F50
Mathematics Subject Classification ID: 65F10
zbMATH DE Number: 1993224
zbMATH Keywords: preconditioning
zbMATH Keywords: incomplete LU factorization
zbMATH Keywords: rational approximation
zbMATH Keywords: Padé approximation
zbMATH Keywords: matrix diagonal shifting
zbMATH Keywords: sparse matrix
zbMATH Keywords: ill-conditioned matrices
zbMATH Keywords: numerical experiments
reviewed by: Liu Xinguo
describes a project that uses: ARMS
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1993224