On the behaviour of approximate Newton methods (Q1067364)

When Newton's method is used for solving nonlinear equations in Banach spaces, at each step of the iterative procedure the solution of a linear equation is requested. When these equations are solved approximately we have a so-called approximate Newton method. The paper is devoted to the study of the convergence properties of such iterations, under Kantorovich type assumptions. Some criteria are given in order to control their convergence and speed of convergence. Moreover, some a posteriori error estimates are proposed. The general results are applied, as example, to Newton-iterative methods.