Inexact Levenberg-Marquardt method for nonlinear equations

In this paper, we present an inexact Levenberg-Marquardt (LM)method for singular system of nonlinear equations, where the LM parameteris chosen as the norm of the function and the trial step is computed approximately. Under the local error bound condition which is weaker than the non-singularity, we show that the new inexact LM method preserves the quadraticconvergence of the traditional LM method where the parameter is chosen to belarger than a positive constant and the Jacobi at the solution is nonsingular.