(untitled) (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)\|_2provides a local error bound for the system of nonlinear equations. Numerical results show that the algorithm performs well.