A numerical study of optimized sparse preconditioners
type: Item
instance of: scholarly article
title: A numerical study of optimized sparse preconditioners
zbMATH Open document ID: 0812.65029
DOI: 10.1007/BF01955867
author: Aslak Tveito
author: Are Magnus Bruaset
published in: BIT
publication date: 1994-09-26T00:00:00Z
review text: The authors are concerned with the existence of optimized preconditioners of either Cholesky factored form or of polynomial form for the preconditioned conjugate gradient method applied to linear systems with symmetric, positive definite coefficient matrices. The Fourier approach for a discretized 2D Poisson equation as a model problem allows the explicit knowledge of the spectrum of the preconditioned stiffness matrix which is the basis to establish specific criteria for the selection of the preconditioner in terms of object functions depending on the preconditioner's parameters. The performance of the resulting preconditioners is investigated by extensive numerical experiments. In accordance with the theory, the main findings are that optimized preconditioners can lead to a reduction of the number of conjugate gradient iterations, but leave the asymptotic convergence rate unchanged.
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65F35
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 65N35
Mathematics Subject Classification ID: 65N22
zbMATH DE Number: 644787
zbMATH Keywords: Fourier method
zbMATH Keywords: optimized preconditioners
zbMATH Keywords: preconditioned conjugate gradient method
zbMATH Keywords: Poisson equation
zbMATH Keywords: performance
zbMATH Keywords: numerical experiments
zbMATH Keywords: convergence
reviewed by: R. H. W. Hoppe
describes a project that uses: Matlab
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 644787