5 papers · 1 filter
Conditioning and interpolation error bounds for second-order Stiefel retractions with closed-form inverses
Rasmus Jensen, Ralf Zimmermann
Retractions provide a computationally efficient alternative to the Riemannian exponential and logarithm maps for practical data-processing tasks on manifolds. In particular, second…
An new polar factor retraction on the Stiefel manifold with closed-form inverse
Rasmus Jensen, Ralf Zimmermann
Retractions are the workhorses in Riemannian computing applications, where computational efficiency is of the essence. This work introduces a new retraction on the compact Stiefel…
Maximum volume coordinates for Grassmann interpolation: Lagrange, Hermite, and errors
Rasmus Jensen, Ralf Zimmermann
We present a novel approach to Riemannian interpolation on the Grassmann manifold. Instead of relying on the Riemannian normal coordinates, i.e. the Riemannian exponential and loga…
Riemannian optimization on the symplectic Stiefel manifold using second-order information
Rasmus Jensen, Ralf Zimmermann
Riemannian optimization is concerned with problems, where the independent variable lies on a smooth manifold. There is a number of problems from numerical linear algebra that fall…
An efficient algorithm for the Riemannian logarithm on the Stiefel manifold for a family of Riemannian metrics
Simon Mataigne, Ralf Zimmermann, Nina Miolane
Since the popularization of the Stiefel manifold for numerical applications in 1998 in a seminal paper from Edelman et al., it has been exhibited to be a key to solve many problems…