SOR as a preconditioner
type: Item
instance of: scholarly article
title: SOR as a preconditioner
zbMATH Open document ID: 0840.65018
DOI: 10.1016/0168-9274(95)00080-E
author: Yanyan Li
published in: Applied Numerical Mathematics
publication date: 1996-06-30T00:00:00Z
review text: The paper contains numerical results concerning the use of successive overrelaxation (SOR) as a preconditioner for the nonsymmetric iterative solvers GMRES and BiCGSTAB. As a test example, the authors choose a 2D convection-diffusion equation on the unit square with Dirichlet boundary conditions discretized by standard five-point finite differences for the principal part and centered differences for the first-order derivatives. The numerical findings indicate that for both the lexicographic and the red-black ordering, multiple SOR preconditioning steps with a relaxation parameter \(\omega\) close to the optimal \(\omega_{\text{opt}}\) can reduce the number of iterations by at least a factor of 2. Moreover, the preconditioned nonsymmetric iterative solvers are robust with respect to \(\omega\) in the range \(\omega < \omega_{\text{opt}}\) but exhibit a very strong sensitivity for \(\omega > \omega_{\text{opt}}\).
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 15A12
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 65N06
Mathematics Subject Classification ID: 65F35
zbMATH DE Number: 826016
zbMATH Keywords: successive overrelaxation
zbMATH Keywords: numerical results
zbMATH Keywords: preconditioner
zbMATH Keywords: nonsymmetric iterative solvers
zbMATH Keywords: GMRES
zbMATH Keywords: BiCGSTAB
zbMATH Keywords: test example
zbMATH Keywords: convection-diffusion equation
zbMATH Keywords: finite differences
zbMATH Keywords: red-black ordering
zbMATH Keywords: multiple SOR preconditioning
reviewed by: R. H. W. Hoppe
MaRDI profile type: Publication
cites work: Q4325973
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cites work: Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems
cites work: Q5639278
full work available at URL: 0168-9274(95)00080-e
OpenAlex ID: W2009209222
description: scientific article; zbMATH DE number 826016