Introducing One Step Back Iterative Approach to Solve Linear and Non Linear Fixed Point Problem

TL;DR

This paper presents a novel iterative method called the one step back approach, which optimizes coordinate selection to improve convergence in solving linear and nonlinear fixed point problems.

Contribution

It introduces a new iterative technique that anticipates outcomes and optimizes coordinate updates, enhancing convergence in fixed point problems.

Findings

Effective in linear fixed point problems

Applicable to nonlinear equations

Improves convergence speed

Abstract

In this paper, we introduce a new iterative method which we call one step back approach: the main idea is to anticipate the consequence of the iterative computation per coordinate and to optimize on the choice of the sequence of the coordinates on which the iterative update computations are done. The method requires the increase of the size of the state vectors and one iteration step loss from the initial vector. We illustrate the approach in linear and non linear iterative equations.