On generalized successive overrelaxation methods for augmented linear systems

doi:10.1007/s00211-005-0643-0

	On generalized successive overrelaxation methods for augmented linear systems
	Bai, ZZ; Parlett, BN ; Wang, ZQ
	2005-11-01
发表期刊	NUMERISCHE MATHEMATIK
ISSN	0029-599X
卷号	102 期号:1 页码:1-38
摘要	For 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.
DOI	10.1007/s00211-005-0643-0
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000233246900001
出版者	SPRINGER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/2013
专题	计算数学与科学工程计算研究所
通讯作者	Bai, ZZ
作者单位	1.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
推荐引用方式 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.