ON THE RADIUS OF CONVERGENCE OF NEWTON'S METHOD UNDER AVERAGE MILD DIFFERENTIABILITY CONDITIONS

Abstract

We provide a local convergence analysis for Newton's method under mild diffferentiability conditions on the operator involved in a Banach space setting. In particular we show that under the same hypotheses and computational cost but using more precise estimates we can provide a larger convergence radius and finer error bounds on the distances involved than before [4], [6], [7]. Some numerical examples are used to further justify the usage of our results over the earlier ones mentioned above.