On semi-convergence of Hermitian and skew-Hermitian splitting methods for singular linear systems

doi:10.1007/s00607-010-0101-4

	On semi-convergence of Hermitian and skew-Hermitian splitting methods for singular linear systems
	Bai, Zhong-Zhi1,2
	2010-09-01
发表期刊	COMPUTING
ISSN	0010-485X
卷号	89 期号:3-4 页码:171-197
摘要	For the singular, non-Hermitian, and positive semidefinite systems of linear equations, we derive necessary and sufficient conditions for guaranteeing the semi-convergence of the Hermitian and skew-Hermitian splitting (HSS) iteration methods. We then investigate the semi-convergence factor and estimate its upper bound for the HSS iteration method. If the semi-convergence condition is satisfied, it is shown that the semi-convergence rate is the same as that of the HSS iteration method applied to a linear system with the coefficient matrix equal to the compression of the original matrix on the range space of its Hermitian part, that is, the matrix obtained from the original matrix by restricting the domain and projecting the range space to the range space of the Hermitian part. In particular, an upper bound is obtained in terms of the largest and the smallest nonzero eigenvalues of the Hermitian part of the coefficient matrix. In addition, applications of the HSS iteration method as a preconditioner for Krylov subspace methods such as GMRES are investigated in detail, and several examples are used to illustrate the theoretical results and examine the numerical effectiveness of the HSS iteration method served either as a preconditioner for GMRES or as a solver.
关键词	Singular linear system Non-Hermitian matrix Positive semidefinite matrix Hermitian and skew-Hermitian splitting Splitting iteration method Semi-convergence Preconditioning matrix Krylov subspace method
DOI	10.1007/s00607-010-0101-4
语种	英语
资助项目	The National Basic Research Program[2005CB321702] ; The China Outstanding Young Scientist Foundation[10525102] ; The National Natural Science Foundation, People's Republic of China[10471146]
WOS研究方向	Computer Science
WOS类目	Computer Science, Theory & Methods
WOS记录号	WOS:000280594700003
出版者	SPRINGER WIEN
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/9395
专题	计算数学与科学工程计算研究所
通讯作者	Bai, Zhong-Zhi
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 100190, Peoples R China 2.Guizhou Normal Univ, Sch Math & Comp Sci, Guiyang 550001, Peoples R China
推荐引用方式 GB/T 7714	Bai, Zhong-Zhi. On semi-convergence of Hermitian and skew-Hermitian splitting methods for singular linear systems[J]. COMPUTING,2010,89(3-4):171-197.
APA	Bai, Zhong-Zhi.(2010).On semi-convergence of Hermitian and skew-Hermitian splitting methods for singular linear systems.COMPUTING,89(3-4),171-197.
MLA	Bai, Zhong-Zhi."On semi-convergence of Hermitian and skew-Hermitian splitting methods for singular linear systems".COMPUTING 89.3-4(2010):171-197.