A Switching-Method for nonlinear systems

A new iterative method is proposed for the solution of nonlinear systems. The method does not use explicit derivative informations and at each iteration automatically selects one of two distinct iterative schemes: a direct search method and a damped approximate Newtonʹs method. So, the method is referred as Switching-Method. It is shown that the method is a global method with quadratic convergence. Numerical results show the very good practical performance of the method.