Newton-like methods for solving underdetermined nonlinear equations with nondifferentiable terms

Abstract

In this paper we consider Newton-like methods for solving underdetermined systems of nonlinear equations with nondifferentiable terms. After presenting local convergence analysis for the methods, we prove a semilocal convergence theorem as well as uniqueness of solution in a generalized sense. Another semilocal convergence theorem for the Newton-chord method is also established. Finally, a numerical example is given.