Unified Semi-local Convergence for Newton’s Method Under Generalized Conditions in Banach Space

Abstract

We present a semilocal convergence analysis for Newton’s method in a Banach space setting. Using the same Lipschitz constants as in earlier studies we extend the applicability of Newton’s method as follows: The convergence domain is extended; the error estimates are tighter and the information on the location of the solution is at least as precise as before. Numerical examples further justify the theoretical results. © 2022, International Publications. All rights reserved.