(???????)A New Modified Levenberg-Marquardt Method for Systems of Nonlinear Equations

Taking a new choice of the LM parameter lambda(k) = mu(k)?J(k)(T) F-k?(delta) with delta is an element of (0, 2], we give a new modified Levenberg-Marquardt method. Under the error bound condition c dist(w, S) < J(w)F-T(w) which is weaker than the nonsingular of Jacobian J(w), we present that the new Levenberg-Marquardt method has at least superlinear convergence when delta is an element of (0, 1) and quadratic convergence when delta is an element of [1, 2], respectively, which indicates that our new Levenberg-Marquardt method is performed for the systems of nonlinear equations. Also, numerical experiments indicate its efficiency on a set of systems of nonlinear equations.