ON THE CONVERGENCE OF NEWTON-LIKE METHODS USING OUTER INVERSES BUT NOT LIPSCHITZ CONDITIONS

Abstract

We provide new semilocal convergence results for Newton-like method using outer inverses but no Lipschitz conditions in a Banach space setting. The first is the Kantorovich-type approach, whereas the second uses our new concept of recurrent functions. Comparisons are given between the two techniques. Our results are compared favorably with earlier ones using the information and requiring the same computational cost. Numerical examples are also provided in this study.