Volume 21, Issue 5
A Modified Levenberg-Marquardt Algorithm for Singular System of Nonlinear Equations
DOI:

J. Comp. Math., 21 (2003), pp. 625-636

Published online: 2003-10

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• Abstract

Based on the work of paprer [1], we propose a modified Levenberg-Marquardt algoithm 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.

• Keywords

Singular nonlinear equations Levenberg-Marquardt method Trust region algorithm Quadratic convergence

@Article{JCM-21-625, author = {Jin-yan Fan}, title = {A Modified Levenberg-Marquardt Algorithm for Singular System of Nonlinear Equations}, journal = {Journal of Computational Mathematics}, year = {2003}, volume = {21}, number = {5}, pages = {625--636}, abstract = { Based on the work of paprer [1], we propose a modified Levenberg-Marquardt algoithm 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. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/10241.html} }
TY - JOUR T1 - A Modified Levenberg-Marquardt Algorithm for Singular System of Nonlinear Equations AU - Jin-yan Fan JO - Journal of Computational Mathematics VL - 5 SP - 625 EP - 636 PY - 2003 DA - 2003/10 SN - 21 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/10241.html KW - Singular nonlinear equations KW - Levenberg-Marquardt method KW - Trust region algorithm KW - Quadratic convergence AB - Based on the work of paprer [1], we propose a modified Levenberg-Marquardt algoithm 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.