Prof. Ralf Zimmermann(Department of Mathematics and Computer Science (IMADA), University of Southern Denmark (SDU), Denmark)
hosted by Seminar Series on Scientific Computing
"How to interpolate low-rank matrix decompositions? Computing the Riemannian normal coordinates in the space of orthogonal frames"
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 totransfer 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-parameterfamily of Riemannian metrics. The findings are illustrated by numerical experiments. We use the Riemannian normal coordinates to constructinterpolated matrix curves, where the sample data matrices stem from the thin, (truncated) singular value decomposition and the compactQR-decomposition, respectively.
|Time:||Thursday, 27.01.2022, 12:00|