Local parametrization of subspaces on matrix manifolds via derivative information. (English) Zbl 1354.65140
Karasözen, Bülent (ed.) et al., Numerical mathematics and advanced applications – ENUMATH 2015. Selected papers based on the presentations at the European conference, Ankara, Turkey, September 14–18, 2015. Cham: Springer (ISBN 978-3-319-39927-0/hbk; 978-3-319-39929-4/ebook). Lecture Notes in Computational Science and Engineering 112, 379-387 (2016).
Summary: 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 a numerical experiment.
For the entire collection see [Zbl 1358.65003].
For the entire collection see [Zbl 1358.65003].
MSC:
| 65K10 | Numerical optimization and variational techniques |
| 93C20 | Control/observation systems governed by partial differential equations |
| 93B11 | System structure simplification |
Keywords:
Stiefel manifold; trajectories; Grassmann manifold; singular value decomposition; local linearization; parametric model reduction; numerical experimentSoftware:
MatlabReferences:
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