ON NEWTON-HSS METHODS FOR SYSTEMS OF NONLINEAR EQUATIONS WITH POSITIVE-DEFINITE JACOBIAN MATRICES

doi:10.4208/jcm.2009.10-m2836

	ON NEWTON-HSS METHODS FOR SYSTEMS OF NONLINEAR EQUATIONS WITH POSITIVE-DEFINITE JACOBIAN MATRICES
	Bai, Zhong-Zhi1 ; Guo, Xue-Ping 2
	2010-03-01
发表期刊	JOURNAL OF COMPUTATIONAL MATHEMATICS
ISSN	0254-9409
卷号	28 期号:2 页码:235-260
摘要	The Hermitian and skew-Hermitian splitting (HSS) method is an unconditionally convergent iteration method for solving large sparse non-Hermitian positive definite system of linear equations. By making use of the HSS iteration as the inner solver for the Newton method, we establish a class of Newton-HSS methods for solving large sparse systems of nonlinear equations with positive definite Jacobian matrices at the solution points. For this class of inexact Newton methods, two types of local convergence theorems are proved under proper conditions, and numerical results are given to examine their feasibility and effectiveness. In addition, the advantages of the Newton-HSS methods over the Newton-USOR., the Newton-GMRES and the Newton-GCG methods are shown through solving Systems of nonlinear equations arising from the finite difference discretization of a two-dimensional convect ion-diffusion equation perturbed by a nonlinear term. The numerical implementations also show that as preconditioners for the Newton-GMRES and the Newton-GCG methods the HSS iteration outperforms the USOR iteration in both computing time and iteration step.
关键词	Systems of nonlinear equations HSS iteration method Newton method Local convergence
DOI	10.4208/jcm.2009.10-m2836
语种	英语
资助项目	National Basic Research Program[2005CB321702] ; China Outstanding Young Scientist Foundation[10525102] ; National Natural Science Foundation, P.R. China[10471146] ; National Natural Science Foundation, P.R. China[10571059] ; National Natural Science Foundation, P.R. China[10571060]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000274262100005
出版者	VSP 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/10343
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, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China 2.E China Normal Univ, Dept Math, Shanghai 200062, Peoples R China
推荐引用方式 GB/T 7714	Bai, Zhong-Zhi,Guo, Xue-Ping. ON NEWTON-HSS METHODS FOR SYSTEMS OF NONLINEAR EQUATIONS WITH POSITIVE-DEFINITE JACOBIAN MATRICES[J]. JOURNAL OF COMPUTATIONAL MATHEMATICS,2010,28(2):235-260.
APA	Bai, Zhong-Zhi,&Guo, Xue-Ping.(2010).ON NEWTON-HSS METHODS FOR SYSTEMS OF NONLINEAR EQUATIONS WITH POSITIVE-DEFINITE JACOBIAN MATRICES.JOURNAL OF COMPUTATIONAL MATHEMATICS,28(2),235-260.
MLA	Bai, Zhong-Zhi,et al."ON NEWTON-HSS METHODS FOR SYSTEMS OF NONLINEAR EQUATIONS WITH POSITIVE-DEFINITE JACOBIAN MATRICES".JOURNAL OF COMPUTATIONAL MATHEMATICS 28.2(2010):235-260.