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Restrictive preconditioners for conjugate gradient methods for symmetric positive definite linear systems
Bai, ZZ; Wang, ZQ
2006-03-15
Source PublicationJOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
ISSN0377-0427
Volume187Issue:2Pages:202-226
AbstractThe restrictively preconditioned conjugate gradient (RPCG) method for solving large sparse system of linear equations of a symmetric positive definite and block two-by-two coefficient matrix is further studied. In fact, this RPCG method is essentially the classical preconditioned conjugate gradient (PCG) method with a specially structured preconditioner. Within this setting, we present algorithmic descriptions of two restrictive preconditioners that, respectively, employ the block Jacobi and the block symmetric Gauss-Seidel matrix splitting matrices as approximations to certain matrices involved in them, and give convergence analyses of the correspondingly induced two PCG methods. Numerical results show that these restrictive preconditioners can lead to practical and effective PCG methods for solving large sparse systems of linear equations of symmetric positive definite and block two-by-two coefficient matrices. (c) 2005 Elsevier B.V. All rights reserved.
Keywordlinear system block two-by-two matrix symmetric positive definite matrix restrictive preconditioner conjugate gradient method
DOI10.1016/j.cam.2005.03.044
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000233952800005
PublisherELSEVIER SCIENCE BV
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/3657
Collection计算数学与科学工程计算研究所
Corresponding AuthorBai, ZZ
AffiliationChinese Acad Sci, State Key Lab Sci, Inst Computat Math & Sci Engn, Acad Math & Syst Sci, Beijing 100080, Peoples R China
Recommended Citation
GB/T 7714
Bai, ZZ,Wang, ZQ. Restrictive preconditioners for conjugate gradient methods for symmetric positive definite linear systems[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,2006,187(2):202-226.
APA Bai, ZZ,&Wang, ZQ.(2006).Restrictive preconditioners for conjugate gradient methods for symmetric positive definite linear systems.JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,187(2),202-226.
MLA Bai, ZZ,et al."Restrictive preconditioners for conjugate gradient methods for symmetric positive definite linear systems".JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 187.2(2006):202-226.
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