ON THE CONVERGENCE OF NEWTON'S METHOD USING THE INVERSE FUNCTION THEOREM

Abstract

We provide a semilocal convergence analysis for Newton's method in a Banach space setting using the inverse function theorem. Using a combination of a Lipschitz as well as a center Lipschitz type condition we provide: weaker sufficient convergence conditions; finer error bounds on the distances involved, and a more precise information on the location of the solution than before [4]-[7]. Moreover, our results are obtained under the same or less computational cost.