A Modified Levenberg-Marquardt Algorithm for Singular System of Nonlinear Equations (Journal of Computational Mathematics, 2021)
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 $F(x):R^n→ R^n$ 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.