Local convergence analysis of Gauss-Newton's method under majorant condition

TL;DR

This paper provides a local convergence analysis of Gauss-Newton's method for nonlinear least squares problems under a majorant condition, establishing optimal convergence radius and solution uniqueness range.

Contribution

It introduces a unified framework for convergence analysis under a majorant condition, improving understanding of Gauss-Newton's method's local behavior.

Findings

Optimal convergence radius determined

Largest range for solution uniqueness identified

Unified previous disparate results

Abstract

The Gauss-Newton's method for solving nonlinear least squares problems is studied in this paper. Under the hypothesis that the derivative of the function associated with the least square problem satisfies a majorant condition, a local convergence analysis is presented. This analysis allow us to obtain the optimal convergence radius, the biggest range for the uniqueness of solution, and to unify two previous and unrelated results.