On HSS-based iteration methods for weakly nonlinear systems

doi:10.1016/j.apnum.2009.06.005

	On HSS-based iteration methods for weakly nonlinear systems
	Bai, Zhong-Zhi; Yang, Xi
	2009-12-01
发表期刊	APPLIED NUMERICAL MATHEMATICS
ISSN	0168-9274
卷号	59 期号:12 页码:2923-2936
摘要	Based oil separable property of the linear and the nonlinear terms and on the Hermitian and skew-Hermitian splitting of the coefficient matrix, we present the Picard-HSS and the nonlinear HSS-like iteration methods for solving a class of large scale systems of weakly nonlinear equations. The advantage of these methods over the Newton and the Newton-HSS iteration methods is that they do not require explicit construction and accurate computation of the Jacobian matrix, and only need to solve linear sub-systems of constant coefficient matrices. Hence, computational workloads and computer memory may be saved in actual implementations. Under suitable conditions, we establish local convergence theorems for both Picard-HSS and nonlinear HSS-like iteration methods. Numerical implementations show that both Picard-HSS and nonlinear HSS-like iteration methods are feasible, effective, and robust nonlinear solvers for this class of large scale systems of weakly nonlinear equations. (C) 2009 Published by Elsevier B.V. oil behalf of IMACS.
关键词	System of weakly nonlinear equations HSS iteration method Inner/outer iteration scheme Nonlinear iteration scheme Local convergence
DOI	10.1016/j.apnum.2009.06.005
语种	英语
资助项目	National Basic Research Program[2005CB321702] ; National Outstanding Young Scientist Foundation[10525102] ; National Natural Science Foundation , PR China[10471146]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000270453100004
出版者	ELSEVIER SCIENCE BV
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/7399
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, Acad Math & Syst Sci, State Key Lab Sci Engn Comp, Inst Computat Math & Sci Engn Comp, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Bai, Zhong-Zhi,Yang, Xi. On HSS-based iteration methods for weakly nonlinear systems[J]. APPLIED NUMERICAL MATHEMATICS,2009,59(12):2923-2936.
APA	Bai, Zhong-Zhi,&Yang, Xi.(2009).On HSS-based iteration methods for weakly nonlinear systems.APPLIED NUMERICAL MATHEMATICS,59(12),2923-2936.
MLA	Bai, Zhong-Zhi,et al."On HSS-based iteration methods for weakly nonlinear systems".APPLIED NUMERICAL MATHEMATICS 59.12(2009):2923-2936.