Convergence of the Gauss-Newton method for a special class of systems of equations under a majorant condition

TL;DR

This paper analyzes the convergence of the Gauss-Newton method for specific nonlinear systems under a majorant condition, providing simplified convergence criteria and applications for particular cases.

Contribution

It introduces a semi-local convergence analysis for the Gauss-Newton method using a majorant condition, simplifying convergence proofs and extending to special cases.

Findings

Convergence regions are characterized by a simple majorant condition.

The analysis simplifies existing convergence proofs.

Applications to specific system classes are demonstrated.

Abstract

In this paper, we study the Gauss-Newton method for a special class of systems of nonlinear equation. Under the hypothesis that the derivative of the function under consideration satisfies a majorant condition, semi-local convergence analysis is presented. In this analysis the conditions and proof of convergence are simplified by using a simple majorant condition to define regions where the Gauss-Newton sequence is "well behaved". Moreover, special cases of the general theory are presented as applications.