A Levenberg-Marquardt algorithm with correction for singular system of nonlinear equations

In this paper we propose a new LM algorithm for the singular system of nonlinear equations F(x)=0, where F(x):R^n->R^n is continuously differentiable and F^'(x) is Lipschitz continuous. At every iteration, not only a LM step but also a correction step are computed. The LM parameter is taken as @m"[email protected]?F"[email protected]?^@d, where @[email protected]?(0,2] and @m"k is updated by the trust region technique. Under the local error bound condition which is weaker than nonsingularity, we prove the convergence rate of the algorithm is min{2,[email protected]}. Numerical results show that the new LM algorithm performs very well.