文献类型：期刊文献

英文题名：Convergence analysis of a variant of the Newton method for solving nonlinear equations

作者：Lin, Yiqin[2];Bao, Liang[1];Jia, Xianzheng[3]

机构：[1]E China Univ Sci & Technol, Dept Math, Shanghai 200237, Peoples R China;[2]Hunan Univ Sci & Engn, Dept Math & Computat Sci, Yongzhou 425100, Peoples R China;[3]Shandong Univ Technol, Sch Sci, Zibo 255049, Peoples R China

年份：2010

卷号：59

期号：6

起止页码：2121

外文期刊名：COMPUTERS & MATHEMATICS WITH APPLICATIONS

收录：;EI(收录号：20100912744059);WOS:【SCI-EXPANDED(收录号:WOS:000279257200024)】；

基金：The authors would like to thank the anonymous referees for their helpful suggestions, which greatly improved the paper. This work was supported by the National Natural Science Foundation of China under grant 10801048 and the Natural Science Foundation of Hunan Province under grant 09JJ6014.

语种：英文

外文关键词：Nonlinear system; Newton method; Modified Newton method; Convergence behavior; Nonsymmetric algebraic Riccati equation; M-matrix

摘要：The paper presents a convergence analysis of a modified Newton method for solving nonlinear systems of equations. The convergence results show that this method converges cubically in the nonsingular case, and linearly with the rate 3/8 under some sufficient conditions when the Jacobian is singular at the root. The convergence theory is used to analyze the convergence behavior when the modified Newton method is applied to a nonsymmetric algebraic Riccati equation arising in transport theory. Numerical experiment confirms the theoretical results. (C) 2009 Elsevier Ltd. All rights reserved.