Iterative solution of strongly nonsymmetric systems of linear algebraic equations
type: Item
instance of: scholarly article
title: Iterative solution of strongly nonsymmetric systems of linear algebraic equations
zbMATH Open document ID: 0946.65018
published in: Computational Mathematics and Mathematical Physics
publication date: 2000-07-04T00:00:00Z
review text: It is well known that most of the widely accepted preconditioners are designed to improve the properties of the symmetric part of system \(Au=b\). It often happens that difficulties are associated with the ill-conditioned skew-symmetric part of the system to be solved. The preconditioner suggested in this paper allows one to solve the problem in the simplest and most natural way. The authors examine the convergence of Richardson's method as applied to the preconditioned system in the case when the original matrix is dissipative. Sufficient conditions for the convergence of the method are presented, a procedure for finding the optimal value of the iteration parameter is developed, and an estimate for the convergence rate is given.
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65F35
zbMATH DE Number: 1467914
zbMATH Keywords: strongly nonsymmetric systems
zbMATH Keywords: ill-conditioned skew-symmetric part
zbMATH Keywords: preconditioner
zbMATH Keywords: Richardson's method
zbMATH Keywords: convergence
author: Mike A. Botchev
author: L. A. Krukier
reviewed by: A. Tret'yakov
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1467914