A MATRIX-ALGEBRAIC ALGORITHM FOR THE RIEMANNIAN LOGARITHM ON THE STIEFEL MANIFOLD UNDER THE CANONICAL METRIC

作者：Zimmermann Ralf^*

来源：SIAM Journal on Matrix Analysis and Applications, 2017, 38(2): 322-342.

DOI：10.1137/16M1074485

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

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.

• 出版日期2017