Tootfinder

A single shooting method with approximate Fr\'{e}chet derivative for computing geodesics on the Stiefel manifold
Marco Sutti
https://arxiv.org/abs/2404.04089

A single shooting method with approximate Fréchet derivative for computing geodesics on the Stiefel manifold
This paper shows how to use the shooting method, a classical numerical algorithm for solving boundary value problems, to compute the Riemannian distance on the Stiefel manifold $ \mathrm{St}(n,p) $, the set of $ n \times p $ matrices with orthonormal columns. The proposed method is a shooting method in the sense of the classical shooting methods for solving boundary value problems; see, e.g., Stoer and Bulirsch, 1991. The main feature is that we provide an approximate formula for the Fréchet d…