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

doi:10.1016/j.laa.2007.02.018

	On inexact Hermitian and skew-Hermitian splitting methods for non-Hermitian positive definite linear systems
	Bai, Zhong-Zhi2 ; Golub, Gene H.3; Ng, Michael K.1
	2008-01-15
发表期刊	LINEAR ALGEBRA AND ITS APPLICATIONS
ISSN	0024-3795
卷号	428 期号:2-3 页码:413-440
摘要	We study theoretical properties of two inexact Hermitian/skew-Hermitian splitting (IHSS) iteration methods for the large sparse non-Hermitian positive definite system of linear equations. In the inner iteration processes, we employ the conjugate gradient (CG) method to solve the linear systems associated with the Hermitian part, and the Lanczos or conjugate gradient for normal equations (CGNE) method to solve the linear systems associated with the skew-Hermitian part, respectively, resulting in IHSS(CG, Lanczos) and IHSS(CG, CGNE) iteration methods, correspondingly. Theoretical analyses show that both IHSS(CG, Lanczos) and IHSS(CG, CGNE) converge unconditionally to the exact solution of the non-Hermitian positive definite linear system. Moreover, their contraction factors and asymptotic convergence rates are dominantly dependent on the spectrum of the Hermitian part, but are less dependent on the spectrum of the skew-Hermitian part, and are independent of the eigenvectors of the matrices involved. Optimal choices of the inner iteration steps in the IHSS(CG, Lanczos) and IHSS(CG, CGNE) iterations are discussed in detail by considering both global convergence speed and overall computation workload, and computational efficiencies of both inexact iterations are analyzed and compared deliberately. (c) 2007 Elsevier Inc. All rights reserved.
关键词	Hermitian matrix skew-Hermitian matrix inexact iterations conjugate gradient (CG) method Lanczos method conjugate gradient for normal equations (CGNE) method
DOI	10.1016/j.laa.2007.02.018
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000252172800003
出版者	ELSEVIER SCIENCE INC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/6827
专题	计算数学与科学工程计算研究所
通讯作者	Ng, Michael K.
作者单位	1.Hong Kong Baptist Univ, Dept Math, Kowloon Tong, Hong Kong, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, State Key Lab Sci Engn Comp, Beijing 100080, Peoples R China 3.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.,Ng, Michael K.. On inexact Hermitian and skew-Hermitian splitting methods for non-Hermitian positive definite linear systems[J]. LINEAR ALGEBRA AND ITS APPLICATIONS,2008,428(2-3):413-440.
APA	Bai, Zhong-Zhi,Golub, Gene H.,&Ng, Michael K..(2008).On inexact Hermitian and skew-Hermitian splitting methods for non-Hermitian positive definite linear systems.LINEAR ALGEBRA AND ITS APPLICATIONS,428(2-3),413-440.
MLA	Bai, Zhong-Zhi,et al."On inexact Hermitian and skew-Hermitian splitting methods for non-Hermitian positive definite linear systems".LINEAR ALGEBRA AND ITS APPLICATIONS 428.2-3(2008):413-440.