On multi-step extended maximum residual Kaczmarz method for solving large inconsistent linear systems

TL;DR

This paper introduces a multi-step extended maximum residual Kaczmarz method for efficiently solving large inconsistent linear systems, demonstrating improved convergence and computational performance over existing methods.

Contribution

The paper proposes a novel multi-step extended maximum residual Kaczmarz method with proven convergence and superior efficiency for large inconsistent linear systems.

Findings

The method converges with an established upper bound on the rate.

Numerical experiments show it outperforms existing Kaczmarz methods.

It reduces the number of iterations and computational costs.

Abstract

A multi-step extended maximum residual Kaczmarz method is presented for the solution of the large inconsistent linear system of equations by using the multi-step iterations technique. Theoretical analysis proves the proposed method is convergent and gives an upper bound on its convergence rate. Numerical experiments show that the proposed method is effective and outperforms the existing extended Kaczmarz methods in terms of the number of iteration steps and the computational costs.