A matrix-algebraic algorithm for the Riemannian logarithm on the Stiefel manifold under the canonical metric
Provides a more efficient alternative to optimization-based methods for computing geodesics on Stiefel manifolds, benefiting applications in optimization, machine learning, and signal processing.
The authors derive a numerical algorithm for evaluating the Riemannian logarithm on the Stiefel manifold under the canonical metric, proving local convergence with linear rate. The algorithm is matrix-algebraic, avoiding optimization-based approaches.
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.