Abstract

Several applications in optimization, image, and signal processing deal with data that belong to the Stiefel manifold St(n,p), that is, the set of n-by-p matrices with orthonormal columns. Some applications, like finding the Riemannian center of mass, require evaluating the geodesic distance between two arbitrary points on St(n,p). Since no explicit formula is known for computing the distance on St(n,p), one has to resort to numerical methods. In this talk, we will see how to use the shooting method, a classical numerical algorithm for solving initial value problems, to compute the distance on St(n,p). We will showcase three example applications in the contexts of shape analysis, summary statistics, and model order reduction.