LOCAL CONVERGENCE ANALYSIS FOR A CERTAIN CLASS OF INEXACT METHODS

Abstract

We provide a local convergence analysis for a certain class inexact methods in a Banach space setting, in order to approximate a solution of a nonlinear equation [6]. The assumptions involve center-Lipschitz-type and radius-Lipschitz-type conditions [15], [8], [5]. Our results have the following advantages (under the same computational cost): larger radii, and finer error bounds on the distances involved than in [8], [15] in many interesting cases. Numerical examples further validating the theoretical results are also provided in this study.