A polynomial preconditioner for the CMRH algorithm
type: Item
instance of: scholarly article
title: A polynomial preconditioner for the CMRH algorithm
zbMATH Open document ID: 1215.65060
DOI: 10.1155/2011/545470
author: Jiangzhou Lai
author: Shiji Xu
author: Linzhang Lu
published in: Mathematical Problems in Engineering
publication date: 2011-06-07T00:00:00Z
full work available at URL: https://eudml.org/doc/231894
review text: Summary: Many large and sparse linear systems can be solved efficiently by restarted GMRES and CMRH methods [\textit{H. Sadok}, Numer. Algorithms 20, No.~4, 303--321 (1999; Zbl 0936.65031)]. The CMRH\((m)\) method is less expensive and requires slightly less storage than GMRES\((m)\). But like GMRES, the restarted CMRH method may not converge. In order to remedy this defect, this paper presents a polynomial preconditioner for CMRH-based algorithm. Numerical experiments are given to show that the polynomial preconditioner is quite simple and easily constructed and the preconditioned CMRH\((m)\) with the polynomial preconditioner has better performance than CMRH\((m)\).
Mathematics Subject Classification ID: 65F10
zbMATH DE Number: 5904902
Wikidata QID: Q58693202
describes a project that uses: CMRH
MaRDI profile type: Publication
OpenAlex ID: W2034237012
cites work: GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
cites work: CMRH: A new method for solving nonsymmetric linear systems based on the Hessenberg reduction algorithm
cites work: A polynomial preconditioner for the GMRES algorithm
cites work: Implementation of an adaptive algorithm for Richardson's method
cites work: A Theoretical Comparison of the Arnoldi and GMRES Algorithms
cites work: Q4178391
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description: scientific article; zbMATH DE number 5904902