Incomplete Semiiterative Methods for Solving Operator Equations in Banach Space

Abstract

There are several methods for solving operator equations in a Banach space. The successive approximation methods require the spectral radius of the iterative operator be less that 1 for convergence.
In this paper, we try to use the incomplete semiiterative methods to solve a linear operator equation in Banach space. Usually the special semiiterative methods are convergent even when the spectral radius of the iterative operator of an operator of an operator equation is greater than 1.