Extended local convergence for Newton-type solver under weak conditions

Abstract

We present the local convergence of a Newton-type solver for equations involving Banach space valued operators. The eighth order of convergence wasshown earlier in the special case of the k-dimensional Euclidean space, usinghypotheses up to the eighth derivative although these derivatives do not appearin the method. We show convergence using only the first derivative. This way weextend the applicability of the methods. Numerical examples are used to showthe convergence conditions. Finally, the basins of attraction of the method, onsome test problems are presented © 2021, Studia Universitatis Babes-Bolyai Mathematica. All Rights Reserved.