TY - JOUR
T1 - A Modified Levenberg-Marquardt Algorithm for Singular System of Nonlinear Equations
AU - Fan , Jin-Yan
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, Levenberg-Marquardt method, Trust region algorithm, Quadratic convergence.
AB - <p style="text-align: justify;">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 $F&#39;(x)$ 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.</p>