Convergence analysis of Riemannian Gauss-Newton methods and its connection with the geometric condition number

TL;DR

This paper analyzes the local convergence of Riemannian Gauss-Newton methods for least squares problems on manifolds and links the convergence constants to the geometric condition number, enhancing understanding of algorithm stability.

Contribution

It provides new estimates for convergence constants of Riemannian Gauss-Newton methods and connects them to the geometric condition number, advancing theoretical insights.

Findings

Convergence constants are explicitly estimated in terms of the geometric condition number.

The analysis offers a deeper understanding of the stability and efficiency of Riemannian Gauss-Newton methods.

The work bridges numerical analysis and differential geometry in the context of optimization algorithms.

Abstract

We obtain estimates of the multiplicative constants appearing in local convergence results of the Riemannian Gauss-Newton method for least squares problems on manifolds and relate them to the geometric condition number of [P. B\"urgisser and F. Cucker, Condition: The Geometry of Numerical Algorithms, 2013].