On solving operator equations by multipoint iterative methods

Abstract

Multipoint iterative procedures for solving non-linear operator equations in Banach spaces are considered. They are described by a general iteration scheme (1.2) which extends that proposed by Wolfe. Local convergence and order of convergence are studied. Moreover error estimates are given. A classical efficiency measure is introduced and criteria for comparing the efficiencies of different families of multipoint iterative methods are established. Later these criteria are applied to some interesting particular cases.