A New Modified Levenberg–Marquardt Method for Systems of Nonlinear Equations

Taking a new choice of the LM parameter λk=μkJkTFkδ with δ∈0,2, we give a new modified Levenberg–Marquardt method. Under the error bound condition c distw,S≤JwTFw which is weaker than the nonsingular of Jacobian Jw, we present that the new Levenberg–Marquardt method has at least superlinear convergence when δ∈0,1 and quadratic convergence when δ∈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.