On successive-overrelaxation acceleration of the Hermitian and skew-Hermitian splitting iterations

doi:10.1002/nla.517

	On successive-overrelaxation acceleration of the Hermitian and skew-Hermitian splitting iterations
	Bai, Zhong-Zhi; Golub, Gene H.; Ng, Michael K.
	2007-05-01
发表期刊	NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS
ISSN	1070-5325
卷号	14 期号:4 页码:319-335
摘要	We further generalize the technique for constructing the Hermitian/skew-Herrnitian splitting (HSS) iteration method for solving large sparse non-Hermitian positive definite system of linear equations to the normal/skew-Hennitian (NS) splitting obtaining a class of normal/skew-Hermitian splitting (NSS) iteration methods. Theoretical analyses show that the NSS method converges unconditionally to the exact solution of thic system of linear equations. Moreover, we derive an upper bound of the contraction factor of the NSS iteration which is dependent solely on the spectrum of the normal splitting matrix, and is independent of the eigenvectors of the matrices involved. We present a successive-overrelaxation (SOR) acceleration scheme for the NSS iteration, which specifically results in an acceleration scheme for the HSS iteration. Convergence conditions for this SOR scheme are derived under the assumption that the eigenvalues of the corresponding block Jacobi iteration matrix lie in certain regions in the complex plane. A numerical example is used to show that the SOR technique can significantly accelerate the convergence rate of the NSS or the HSS iteration method. Copyright (c) 2006 John Wiley & Sons, Ltd.
关键词	non-Hermitian matrix normal matrix Hermitian matrix skew-Hermitian matrix splitting iteration method successive overrelaxation
DOI	10.1002/nla.517
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000245958400005
出版者	JOHN WILEY & SONS LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/4403
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	Chinese Acad Sci, State Key Lab Sci Engn Comp, Inst Computat Math & Sci Engn Comp, Acad Math & Syst Sci, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Bai, Zhong-Zhi,Golub, Gene H.,Ng, Michael K.. On successive-overrelaxation acceleration of the Hermitian and skew-Hermitian splitting iterations[J]. NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS,2007,14(4):319-335.
APA	Bai, Zhong-Zhi,Golub, Gene H.,&Ng, Michael K..(2007).On successive-overrelaxation acceleration of the Hermitian and skew-Hermitian splitting iterations.NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS,14(4),319-335.
MLA	Bai, Zhong-Zhi,et al."On successive-overrelaxation acceleration of the Hermitian and skew-Hermitian splitting iterations".NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS 14.4(2007):319-335.