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A globally convergent Newton-GMRES method for large sparse systems of nonlinear equations
An, Heng-Bin; Bai, Zhong-Zhi
2007-03-01
Source PublicationAPPLIED NUMERICAL MATHEMATICS
ISSN0168-9274
Volume57Issue:3Pages:235-252
AbstractThe 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.
Keywordsystems of nonlinear equations inexact Newton method GMRES global convergence
DOI10.1016/j.apnum.2006.02.007
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000244648600001
PublisherELSEVIER SCIENCE BV
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/4071
Collection计算数学与科学工程计算研究所
Corresponding AuthorBai, Zhong-Zhi
AffiliationChinese Acad Sci, State Key Lab Sci Engn Comp, Inst Computat Math & Sci Engn Comp, Acad Math & Syst Sci, Beijing 100080, Peoples R China
Recommended Citation
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.
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