A Polynomial Preconditioned Global CMRH Method for Linear Systems with Multiple Right-Hand Sides

A Polynomial Preconditioned Global CMRH Method for Linear Systems with Multiple Right-Hand Sides

The restarted global CMRH method (Gl-CMRH(m)) (Heyouni, 2001) is an attractive method for linear systems with multiple right-hand sides. However, Gl-CMRH(m) may converge slowly or even stagnate due to a limited Krylov subspace. To ameliorate this drawback, a polynomial preconditioned variant of Gl-C...

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Main Authors: Ke Zhang, Chuanqing Gu
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2013/457089
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spelling doaj-d2b594b381724fa2b1237983d0c653fb2020-11-24T23:01:19ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/457089457089A Polynomial Preconditioned Global CMRH Method for Linear Systems with Multiple Right-Hand SidesKe Zhang0Chuanqing Gu1Department of Mathematics, Shanghai University, Shanghai 200444, ChinaDepartment of Mathematics, Shanghai University, Shanghai 200444, ChinaThe restarted global CMRH method (Gl-CMRH(m)) (Heyouni, 2001) is an attractive method for linear systems with multiple right-hand sides. However, Gl-CMRH(m) may converge slowly or even stagnate due to a limited Krylov subspace. To ameliorate this drawback, a polynomial preconditioned variant of Gl-CMRH(m) is presented. We give a theoretical result for the square case that assures that the number of restarts can be reduced with increasing values of the polynomial degree. Numerical experiments from real applications are used to validate the effectiveness of the proposed method.http://dx.doi.org/10.1155/2013/457089
collection DOAJ
language English
format Article
sources DOAJ
author Ke Zhang
Chuanqing Gu
spellingShingle Ke Zhang
Chuanqing Gu
A Polynomial Preconditioned Global CMRH Method for Linear Systems with Multiple Right-Hand Sides
Journal of Applied Mathematics
author_facet Ke Zhang
Chuanqing Gu
author_sort Ke Zhang
title A Polynomial Preconditioned Global CMRH Method for Linear Systems with Multiple Right-Hand Sides
title_short A Polynomial Preconditioned Global CMRH Method for Linear Systems with Multiple Right-Hand Sides
title_full A Polynomial Preconditioned Global CMRH Method for Linear Systems with Multiple Right-Hand Sides
title_fullStr A Polynomial Preconditioned Global CMRH Method for Linear Systems with Multiple Right-Hand Sides
title_full_unstemmed A Polynomial Preconditioned Global CMRH Method for Linear Systems with Multiple Right-Hand Sides
title_sort polynomial preconditioned global cmrh method for linear systems with multiple right-hand sides
publisher Hindawi Limited
series Journal of Applied Mathematics
issn 1110-757X
1687-0042
publishDate 2013-01-01
description The restarted global CMRH method (Gl-CMRH(m)) (Heyouni, 2001) is an attractive method for linear systems with multiple right-hand sides. However, Gl-CMRH(m) may converge slowly or even stagnate due to a limited Krylov subspace. To ameliorate this drawback, a polynomial preconditioned variant of Gl-CMRH(m) is presented. We give a theoretical result for the square case that assures that the number of restarts can be reduced with increasing values of the polynomial degree. Numerical experiments from real applications are used to validate the effectiveness of the proposed method.
url http://dx.doi.org/10.1155/2013/457089
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AT chuanqinggu apolynomialpreconditionedglobalcmrhmethodforlinearsystemswithmultiplerighthandsides
AT kezhang polynomialpreconditionedglobalcmrhmethodforlinearsystemswithmultiplerighthandsides
AT chuanqinggu polynomialpreconditionedglobalcmrhmethodforlinearsystemswithmultiplerighthandsides
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