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

For researchers in optimization on manifolds, this work offers a refined theoretical understanding of Gauss-Newton convergence, but the results are incremental as they extend existing theory with explicit constants.

The paper provides explicit estimates for the convergence constants of Riemannian Gauss-Newton methods for least squares on manifolds, linking them to the geometric condition number. The analysis yields tighter bounds than previous work, with the condition number directly influencing the convergence radius and rate.