English

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