A matrix-algebraic algorithm for the Riemannian logarithm on the Stiefel manifold under the canonical metric
Numerical Analysis
2017-03-20 v5 Differential Geometry
Abstract
We derive a numerical algorithm for evaluating the Riemannian logarithm on the Stiefel manifold with respect to the canonical metric. In contrast to the existing optimization-based approach, we work from a purely matrix-algebraic perspective. Moreover, we prove that the algorithm converges locally and exhibits a linear rate of convergence.
Keywords
Cite
@article{arxiv.1604.05054,
title = {A matrix-algebraic algorithm for the Riemannian logarithm on the Stiefel manifold under the canonical metric},
author = {Ralf Zimmermann},
journal= {arXiv preprint arXiv:1604.05054},
year = {2017}
}
Comments
30 pages, 5 figures, Matlab code