Convergence analysis of a variant of the Newton method for solving nonlinear equations

Authors:
Yiqin Lin;Liang Bao;Xianzheng Jia
Affiliations:
Department of Mathematics and Computational Science, Hunan University of Science and Engineering, Yongzhou 425100, PR China;Department of Mathematics, East China University of Science and Technology, Shanghai 200237, PR China;School of Science, Shandong University of Technology, Zibo 255049, PR China
Venue:
Computers & Mathematics with Applications
Year:
2010

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Abstract

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.