Local parametrization of subspaces on matrix manifolds via derivative information

Abstract

A method is proposed for constructing local parametrizations of orthogonal bases and of subspaces by computing trajectories in the Stiefel and the Grassmann manifold, respectively. The trajectories are obtained by exploiting sensitivity information on the singular value decomposition with respect to parametric changes and a Taylor-like local linearization suitably adapted to the underlying manifold structure. An important practical application of the proposed approach is parametric model reduction (pMOR). The connection with pMOR is discussed in detail and the results are illustrated by numerical experiment.