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On generalized successive overrelaxation methods for augmented linear systems
Bai, ZZ; Parlett, BN; Wang, ZQ
2005-11-01
Source PublicationNUMERISCHE MATHEMATIK
ISSN0029-599X
Volume102Issue:1Pages:1-38
AbstractFor the augmented system of linear equations, Golub, Wu and Yuan recently studied an SOR-like method (BIT 41(2001)71-85). By further accelerating it with another parameter, in this paper we present a generalized SOR (GSOR) method for the augmented linear system. We prove its convergence under suitable restrictions on the iteration parameters, and determine its optimal iteration parameters and the corresponding optimal convergence factor. Theoretical analyses show that the GSOR method has faster asymptotic convergence rate than the SOR-like method. Also numerical results show that the GSOR method is more effective than the SOR-like method when they are applied to solve the augmented linear system. This GSOR method is further generalized to obtain a framework of the relaxed splitting iterative methods for solving both symmetric and nonsymmetric augmented linear systems by using the techniques of vector extrapolation, matrix relaxation and inexact iteration. Besides, we also demonstrate a complete version about the convergence theory of the SOR-like method.
DOI10.1007/s00211-005-0643-0
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000233246900001
PublisherSPRINGER
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/2013
Collection计算数学与科学工程计算研究所
Corresponding AuthorBai, ZZ
Affiliation1.Chinese Acad Sci, State Key Lab Sci Engn Comp, Inst Computat Math & Sci Engn Comp, Acad Math & Syst Sci, Beijing 100080, Peoples R China
2.Univ Calif Berkeley, Dept Math, Berkeley, CA 94720 USA
3.Univ Calif Berkeley, Div Comp Sci, Dept EECS, Berkeley, CA 94720 USA
Recommended Citation
GB/T 7714
Bai, ZZ,Parlett, BN,Wang, ZQ. On generalized successive overrelaxation methods for augmented linear systems[J]. NUMERISCHE MATHEMATIK,2005,102(1):1-38.
APA Bai, ZZ,Parlett, BN,&Wang, ZQ.(2005).On generalized successive overrelaxation methods for augmented linear systems.NUMERISCHE MATHEMATIK,102(1),1-38.
MLA Bai, ZZ,et al."On generalized successive overrelaxation methods for augmented linear systems".NUMERISCHE MATHEMATIK 102.1(2005):1-38.
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