On the convergence of levenberg-marquardt method for solving nonlinear systems

Abstract

Levenberg-Marquardt (L-M forshort) method is one of the most important methods for solving systems of nonlinear equations. In this paper, we consider the convergence under λk = min(║Fk║, ║JTk Fk║) of L-M method. We will show that if ║F(xk)║ provides a local error bound, which is weaker than the condition of nonsingularity for the system of nonlinear equations, the sequence generated by the L-M method converges to the point of the solution set quadratically. As well, numerical experiments are reported.