On the Convergence of a New Levenberg-Marquardt Method

We propose a new way to choose the parameter in the Levenberg-Marquardt method for solving nonlinear equations F (x) = 0, where F (x) : R is continuously differentiable and F (x) is Lipschitz continuous. The sequence generated by the new method converges to the solution quadratically, if jjF (x)jj 2 provides a local error bound for the system of nonlinear equations. Numerical results show that the method performs well for singular problems