A matrix-algebraic algorithm for the Riemannian logarithm on the Stiefel   manifold under the canonical metric
  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. 
Ralf Zimmermann
math.NA math.DG