A Matrix-Algebraic Algorithm for the Riemannian Logarithm on the Stiefel Manifold under the Canonical Metric

DOI10.1137/16M1074485zbMath1365.65137arXiv1604.05054WikidataQ115246956 ScholiaQ115246956MaRDI QIDQ5346756

Ralf Zimmermann

Publication date: 29 May 2017

Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1604.05054

zbMATH Keywords

algorithmconvergenceStiefel manifoldRiemannian exponentialBaker-Campbell-Hausdorff seriesGoldberg seriesRiemannian logarithmDynkin series

Mathematics Subject Classification ID

Computation of special functions and constants, construction of tables (65D20) Numerical approximation and evaluation of special functions (33F05) Higher logarithm functions (33B30) Matrix exponential and similar functions of matrices (15A16) Numerical computation of matrix exponential and similar matrix functions (65F60)

Related Items (11)

Introduction to Riemannian Geometry and Geometric Statistics: From Basic Theory to Implementation with Geomstats ⋮ Computing the Riemannian Logarithm on the Stiefel Manifold: Metrics, Methods, and Performance ⋮ Closed-form geodesics and optimization for Riemannian logarithms of Stiefel and flag manifolds ⋮ Endpoint Geodesics on the Stiefel Manifold Embedded in Euclidean Space ⋮ A Riemannian stochastic representation for quantifying model uncertainties in molecular dynamics simulations ⋮ Convergence Analysis of Leapfrog for Geodesics ⋮ Hermite Interpolation and Data Processing Errors on Riemannian Matrix Manifolds ⋮ Statistics on the Stiefel manifold: theory and applications ⋮ Energy-preserving methods on Riemannian manifolds ⋮ 7 Manifold interpolation ⋮ Efficient quasi-geodesics on the Stiefel manifold

Uses Software

• Matlab
• mftoolbox

Cites Work

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• The formal power series for \(\log\,e^x e^y\)
• Convergence proof for Goldberg's exponential series
• Riemannian geometry of Grassmann manifolds with a view on algorithmic computation
• Simplifying the Reinsch algorithm for the Baker–Campbell–Hausdorff series
• A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems
• Convergence domains for the campbell-baker-hausdorff formula
• The Geometry of Algorithms with Orthogonality Constraints
• Functions of Matrices
• Multiscale Representations for Manifold-Valued Data

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