On the complexity of a unified convergence analysis for iterative methods

Abstract

A local and a semi-local convergence of general iterative methods for solving nonlinear operator equations in Banach spaces is developed under ω-continuity conditions. Our approach unifies existing results and provides a new way of studying iterative methods. The main idea is to find a more accurate domain containing the iterates. No extra effort is used to obtain this. Also, the results of the numerical experiments are given that confirm obtained theoretical estimates.