A string averaging method based on strictly quasi-nonexpansive operators with generalized relaxation

TL;DR

This paper introduces a new fixed point iterative method that uses string averaging of strictly quasi-nonexpansive operators with generalized relaxation, applicable to linear systems, convex feasibility, and image reconstruction.

Contribution

It proposes a novel string averaging iterative method based on generalized relaxation for strictly quasi-nonexpansive operators, expanding the toolkit for solving various mathematical problems.

Findings

The method effectively solves linear systems and inequalities.

It improves convergence in convex feasibility problems.

Experimental results demonstrate enhanced performance in image reconstruction.

Abstract

We study a fixed point iterative method based on generalized relaxation of strictly quasi-nonexpansive operators. The iterative method is assembled by averaging of strings, and each string is composed of finitely many strictly quasi-nonexpansive operators. To evaluate the study, we examine a wide class of iterative methods for solving linear systems of equations (inequalities) and the subgradient projection method for solving nonlinear convex feasibility problems. The mathematical analysis is complemented by some experiments in image reconstruction from projections and classical examples, which illustrate the performance using generalized relaxation.