A globally convergent Newton-GMRES method for large sparse systems of nonlinear equations

doi:10.1016/j.apnum.2006.02.007

	A globally convergent Newton-GMRES method for large sparse systems of nonlinear equations
	An, Heng-Bin; Bai, Zhong-Zhi
	2007-03-01
发表期刊	APPLIED NUMERICAL MATHEMATICS
ISSN	0168-9274
卷号	57 期号:3 页码:235-252
摘要	The inexact Newton with backtracking (INB) method is a powerful tool for solving large sparse systems of nonlinear equations. In particular, if the generalized minimal residual (GMRES) method is used to solve the Newton equations, then the Newton-GMRES with backtracking (NGB) method is obtained. In this paper, we present a new class of globally convergent Newton-GMRES methods. In these methods, the typical backtracking strategy is augmented with a new strategy that is invoked when the inexact Newton direction is not satisfactory. Global convergence properties of the proposed methods are established and numerical results are provided, showing that the new method, called the Newton-GMRES with quasi-conjugate-gradient backtracking (NGQCGB), is very robust and effective. (c) 2006 Published by Elsevier B.V. on behalf of IMACS.
关键词	systems of nonlinear equations inexact Newton method GMRES global convergence
DOI	10.1016/j.apnum.2006.02.007
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000244648600001
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/4071
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, State Key Lab Sci Engn Comp, Inst Computat Math & Sci Engn Comp, Acad Math & Syst Sci, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	An, Heng-Bin,Bai, Zhong-Zhi. A globally convergent Newton-GMRES method for large sparse systems of nonlinear equations[J]. APPLIED NUMERICAL MATHEMATICS,2007,57(3):235-252.
APA	An, Heng-Bin,&Bai, Zhong-Zhi.(2007).A globally convergent Newton-GMRES method for large sparse systems of nonlinear equations.APPLIED NUMERICAL MATHEMATICS,57(3),235-252.
MLA	An, Heng-Bin,et al."A globally convergent Newton-GMRES method for large sparse systems of nonlinear equations".APPLIED NUMERICAL MATHEMATICS 57.3(2007):235-252.