On averaging block Kaczmarz methods for solving nonlinear systems of equations

TL;DR

This paper introduces a new class of averaging block nonlinear Kaczmarz methods for solving nonlinear systems, providing convergence analysis and demonstrating superior efficiency over existing methods through numerical experiments.

Contribution

The paper develops a novel averaging block nonlinear Kaczmarz method with proven convergence and improved performance compared to prior approaches.

Findings

Convergence established under suitable assumptions.

Method outperforms existing nonlinear Kaczmarz methods.

Effective with both constant and adaptive stepsizes.

Abstract

A class of averaging block nonlinear Kaczmarz methods is developed for the solution of the nonlinear system of equations. The convergence theory of the proposed method is established under suitable assumptions and the upper bounds of the convergence rate for the proposed method with both constant stepsize and adaptive stepsize are derived. Numerical experiments are presented to verify the efficiency of the proposed method, which outperforms the existing nonlinear Kaczmarz methods in terms of the number of iteration steps and computational costs.