Local Convergence Properties Of The Levenberg-Marquardt Method For Nonlinear Equations Under A Weaker Local Error Bound Condition

This paper mainly considers local convergence properties of theLevenberg-Marquardt method for nonlinear equations. In recent years, manyresearchers have proved that Levenberg-Marquardt method has a quadratic con-vergence rate under a local error bound condition. In this paper, the local errorbound condition is weakened and the Levenberg-Marquardt method is proved tohave a superlinear convergence rate under the weakened error bound condition.Otherwise, we present a Levenberg-Marquardt algorithm with Armijo line searchand narrate the conclusions about its global convergence briefly.