Year: 2003
Author: Jin-Yan Fan
Journal of Computational Mathematics, Vol. 21 (2003), Iss. 5 : pp. 625–636
Abstract
Based on the work of paper [1], we propose a modified Levenberg-Marquardt algorithm for solving singular system of nonlinear equations $F(x)=0$, where $F(x):R^n\rightarrow R^n$ is continuously differentiable and $F'(x)$ is Lipschitz continuous. The algorithm is equivalent to a trust region algorithm in some sense , and the global convergence result is given. The sequence generated by the algorithm converges to the solution quadratically, if $\|F(x)\|_2$provides a local error bound for the system of nonlinear equations. Numerical results show that the algorithm performs well.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2003-JCM-10241
Journal of Computational Mathematics, Vol. 21 (2003), Iss. 5 : pp. 625–636
Published online: 2003-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 12
Keywords: Singular nonlinear equations Levenberg-Marquardt method Trust region algorithm Quadratic convergence.