Accelerated Hermitian and skew-Hermitian splitting iteration methods for saddle-point problems

doi:10.1093/imanum/drl017

	Accelerated Hermitian and skew-Hermitian splitting iteration methods for saddle-point problems
	Bai, Zhong-Zhi; Golub, Gene H.
	2007
发表期刊	IMA JOURNAL OF NUMERICAL ANALYSIS
ISSN	0272-4979
卷号	27 期号:1 页码:1-23
摘要	We establish a class of accelerated Hermitian and skew-Hermitian splitting (AHSS) iteration methods for large sparse saddle-point problems by making use of the Hermitian and skew-Hermitian splitting (HSS) iteration technique. These methods involve two iteration parameters whose special choices can recover the known preconditioned HSS iteration methods, as well as yield new ones. Theoretical analyses show that the new methods converge unconditionally to the unique solution of the saddle-point problem. Moreover, the optimal choices of the iteration parameters involved and the corresponding asymptotic convergence rates of the new methods are computed exactly. In addition, theoretical properties of the preconditioned Krylov subspace methods such as GMRES are investigated in detail when the AHSS iterations are employed as their preconditioners. Numerical experiments confirm the correctness of the theory and the effectiveness of the methods.
关键词	saddle-point problem Hermitian and skew-Hermitian splitting splitting iteration method preconditioning
DOI	10.1093/imanum/drl017
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000243861300001
出版者	OXFORD UNIV PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/3978
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 100080, Peoples R China 2.Stanford Univ, Dept Comp Sci, Sci Comp & Computat Math Program, Stanford, CA 94305 USA
推荐引用方式 GB/T 7714	Bai, Zhong-Zhi,Golub, Gene H.. Accelerated Hermitian and skew-Hermitian splitting iteration methods for saddle-point problems[J]. IMA JOURNAL OF NUMERICAL ANALYSIS,2007,27(1):1-23.
APA	Bai, Zhong-Zhi,&Golub, Gene H..(2007).Accelerated Hermitian and skew-Hermitian splitting iteration methods for saddle-point problems.IMA JOURNAL OF NUMERICAL ANALYSIS,27(1),1-23.
MLA	Bai, Zhong-Zhi,et al."Accelerated Hermitian and skew-Hermitian splitting iteration methods for saddle-point problems".IMA JOURNAL OF NUMERICAL ANALYSIS 27.1(2007):1-23.