AN EXTENSION OF A THEOREM BY B.T. POLYAK ON GRADIENT-TYPE METHODS

Abstract

We extend the applicability of semilocal convergence results by B.T. Polyak for solving nonlinear equations in a Banach space setting [16]. Our idea uses the center-Lipschitz instead of the Lipschitz condition in the convergence analysis of the iterative procedure involved. Numerical examples are presented to show that the earlier results cannot apply but the new results can apply to solve equations.