Hybrid Iterative Methods for Solving Nonlinear Equations in Banach Spaces

Abstract

The present article contributes to the solution of equations which carry the symmetry property of the problem or not. Iterative methods with in- verses generate sequences converging faster to a solution of an equation than methods without inverses. However, the implementation of these methods has drawbacks, since the analytical form of these inverse may be unavailable or computationally very expensive. This problem is addressed in this paper by replacing the inverse with a finite sum of linear opera- tors. A convergence analysis is developed for the hybrid methods. The numerical examples demonstrate that the number of iterates is essentially the same between the hybrid and the original method. This technique is also extended to solve generalized equations.