Hermitian and skew-Hermitian splitting methods for non-hermitian positive definite linear systems

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	Hermitian and skew-Hermitian splitting methods for non-hermitian positive definite linear systems
	Bai, ZZ ; Golub, GH ; Ng, MK
	2003
发表期刊	SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
ISSN	0895-4798
卷号	24 期号:3 页码:603-626
摘要	We study efficient iterative methods for the large sparse non-Hermitian positive definite system of linear equations based on the Hermitian and skew-Hermitian splitting of the coefficient matrix. These methods include a Hermitian/skew-Hermitian splitting (HSS) iteration and its inexact variant, the inexact Hermitian/skew-Hermitian splitting (IHSS) iteration, which employs some Krylov subspace methods as its inner iteration processes at each step of the outer HSS iteration. Theoretical analyses show that the HSS method converges unconditionally to the unique solution of the system of linear equations. Moreover, we derive an upper bound of the contraction factor of the HSS iteration which is dependent solely on the spectrum of the Hermitian part and is independent of the eigenvectors of the matrices involved. Numerical examples are presented to illustrate the effectiveness of both HSS and IHSS iterations. In addition, a model problem of a three-dimensional convection-diffusion equation is used to illustrate the advantages of our methods.
关键词	non-Hermitian matrix splitting Hermitian matrix skew-Hermitian matrix iterative methods
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000181153600001
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/19011
专题	中国科学院数学与系统科学研究院
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.Stanford Univ, Dept Comp Sci, Stanford, CA 94305 USA 3.Univ Hong Kong, Dept Math, Hong Kong, Hong Kong, Peoples R China
推荐引用方式 GB/T 7714	Bai, ZZ,Golub, GH,Ng, MK. Hermitian and skew-Hermitian splitting methods for non-hermitian positive definite linear systems[J]. SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS,2003,24(3):603-626.
APA	Bai, ZZ,Golub, GH,&Ng, MK.(2003).Hermitian and skew-Hermitian splitting methods for non-hermitian positive definite linear systems.SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS,24(3),603-626.
MLA	Bai, ZZ,et al."Hermitian and skew-Hermitian splitting methods for non-hermitian positive definite linear systems".SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS 24.3(2003):603-626.