A matrix-algebraic algorithm for the Riemannian logarithm on the Stiefel manifold under the canonical metric

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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.

Original languageEnglish
JournalSIAM Journal on Matrix Analysis and Applications
Volume38
Issue number2
Pages (from-to)322-342
ISSN0895-4798
DOIs
Publication statusPublished - 2017

Keywords

  • Stiefel manifold
  • Riemannian logarithm
  • Dynkin series
  • Goldberg series
  • Baker-Campbell-Hausdorff
  • Riemannian exponential
  • Baker-Campbell-Hausdorff series

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