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We derive a numerical algorithm for evaluating the Riemannian logarithm onthe Stiefel manifold with respect to the canonical metric. In contrast to theexisting optimization-based approach, we work from a purely matrix-algebraicperspective. Moreover, we prove that the algorithm converges locally andexhibits a linear rate of convergence.

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