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.

Keywords:

• Iterative methods
• non-linear equations
• efficiency of algorithms

C.R. Categories:

• 5.15
• 5.25