Block triangular and skew-Hermitian splitting methods for positive-definite linear systems

doi:10.1137/S1064827503428114

	Block triangular and skew-Hermitian splitting methods for positive-definite linear systems
	Bai, ZZ; Golub, GH ; Lu, LZ ; Yin, JF
	2005
发表期刊	SIAM JOURNAL ON SCIENTIFIC COMPUTING
ISSN	1064-8275
卷号	26 期号:3 页码:844-863
摘要	By further generalizing the concept of Hermitian (or normal) and skew-Hermitian splitting for a non-Hermitian and positive-definite matrix, we introduce a new splitting, called positive-definite and skew-Hermitian splitting (PSS), and then establish a class of PSS methods similar to the Hermitian (or normal) and skew-Hermitian splitting (HSS or NSS) method for iteratively solving the positive-definite systems of linear equations. Theoretical analysis shows that the PSS method converges unconditionally to the exact solution of the linear system, with the upper bound of its convergence factor dependent only on the spectrum of the positive-definite splitting matrix and independent of the spectrum of the skew-Hermitian splitting matrix as well as the eigenvectors of all matrices involved. When we specialize the PSS to block triangular ( or triangular) and skew-Hermitian splitting (BTSS or TSS), the PSS method naturally leads to a BTSS or TSS iteration method, which may be more practical and efficient than the HSS and NSS iteration methods. Applications of the BTSS method to the linear systems of block two-by-two structures are discussed in detail. Numerical experiments further show the effectiveness of our new methods.
关键词	non-Hermitian matrix positive-definite matrix triangular matrix block triangular matrix Hermitian and skew-Hermitian splitting splitting iteration method
DOI	10.1137/S1064827503428114
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000227761300006
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/1414
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, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, State Key Lab Sci Engn Comp, Beijing 100080, Peoples R China 2.Stanford Univ, Dept Comp Sci, Sci Comp & Computat Math Program, Stanford, CA 94305 USA 3.Xiamen Univ, Dept Math, Xiamen 361005, Peoples R China
推荐引用方式 GB/T 7714	Bai, ZZ,Golub, GH,Lu, LZ,et al. Block triangular and skew-Hermitian splitting methods for positive-definite linear systems[J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING,2005,26(3):844-863.
APA	Bai, ZZ,Golub, GH,Lu, LZ,&Yin, JF.(2005).Block triangular and skew-Hermitian splitting methods for positive-definite linear systems.SIAM JOURNAL ON SCIENTIFIC COMPUTING,26(3),844-863.
MLA	Bai, ZZ,et al."Block triangular and skew-Hermitian splitting methods for positive-definite linear systems".SIAM JOURNAL ON SCIENTIFIC COMPUTING 26.3(2005):844-863.