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

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. Bürgisser and F. Cucker, Condition: The Geometry of Numerical Algorithms, 2013].

References in corpus (3)

• An algorithm for generic and low-rank specific identifiability of complex tensors
• The condition number of join decompositions
• A Riemannian Trust Region Method for the Canonical Tensor Rank Approximation Problem

Cited by in corpus (9)

• The condition number of join decompositions
• A Riemannian Trust Region Method for the Canonical Tensor Rank Approximation Problem
• The condition number of Riemannian approximation problems
• Low-rank Tensor Estimation via Riemannian Gauss-Newton: Statistical Optimality and Second-Order Convergence
• Recursive Importance Sketching for Rank Constrained Least Squares: Algorithms and High-order Convergence
• The average condition number of most tensor rank decomposition problems is infinite
• On the average condition number of tensor rank decompositions
• The condition number of many tensor decompositions is invariant under Tucker compression
• Tensor Decompositions for Count Data that Leverage Stochastic and Deterministic Optimization