Prof. Ralf Zimmermann, Department of Mathematics and Computer Science (IMADA), University of Southern Denmark (SDU), Denmark

Title:
How to interpolate low-rank matrix decompositions? Computing the Riemannian normal coordinates in the space of orthogonal frames

Abstract:

We address the problem of computing Riemannian normal coordinates on the real, compact Stiefel manifold of orthogonal frames. The Riemannian normal coordinates are based on the so-called Riemannian exponential and the Riemannian logarithm maps and enable to transfer almost any computational procedure to the realm of the Stiefel manifold. To compute the Riemannian logarithm is to solve the (local) geodesic endpoint problem.

In this talk, we present efficient matrix-algorithms for solving the
geodesic endpoint problem on the Stiefel manifold for a one-parameter
family of Riemannian metrics. The findings are illustrated by numerical experiments. We use the Riemannian normal coordinates to construct interpolated matrix curves, where the sample data matrices stem from the thin, (truncated) singular value decomposition and the compact QR-decomposition, respectively.

How to join

The talk is held online via Zoom. You can join with the following link:
https://uni-kl-de.zoom.us/j/63565018552?pwd=d2VvMENEN1QvNkhlS01helUwRGhYdz09