Generalized Relaxation of a Class of Operators for Solving Convex Feasibility Problem

In this paper, we study a fixed point iteration method based on generalized relaxation of string averaging operator. The string averaging operator will be constructed such a way that each string be made by composition of finitely many strictly quasi-nonexpansive operators. The constructed iterative method includes wide class of iterative methods for solving linear systems of equations (inequalities) and fixed-point iterations for solving nonlinear convex feasibility problems. To illustrate the performance of using generalized relaxation, some experiments in image reconstruction from projections is presented.

Keywords:

Convex feasibility problem , Generalized relaxation , Quasi-nonexpansive operators , String averaging