Abstract
One approach to parametric and adaptive model reduction is via the interpolation
of orthogonal bases, subspaces or positive definite system matrices. In all
these cases, the sampled inputs stem from matrix sets that feature a geometric structure
and thus form so-called matrix manifolds. This chapter reviews the numerical
treatment of the most important matrix manifolds that arise in the context of model
reduction. Moreover, the principal approaches to data interpolation and Taylor-like
extrapolation on matrix manifolds are outlined and complemented by algorithms in
pseudo-code.
of orthogonal bases, subspaces or positive definite system matrices. In all
these cases, the sampled inputs stem from matrix sets that feature a geometric structure
and thus form so-called matrix manifolds. This chapter reviews the numerical
treatment of the most important matrix manifolds that arise in the context of model
reduction. Moreover, the principal approaches to data interpolation and Taylor-like
extrapolation on matrix manifolds are outlined and complemented by algorithms in
pseudo-code.
| Original language | English |
|---|---|
| Title of host publication | Model Order Reduction : Volume 1 System- and Datat Driven Methods and Algorithms |
| Editors | Peter Benner |
| Volume | 1 |
| Publisher | De Gruyter |
| Publication date | 8. Nov 2021 |
| Pages | 229-274 |
| Chapter | 7 |
| ISBN (Print) | 9783110500431 |
| ISBN (Electronic) | 9783110498967 |
| DOIs | |
| Publication status | Published - 8. Nov 2021 |
Bibliographical note
Published Version of the ArXiv preprint"Manifold Interpolation and Model Reduction".
Keywords
- Interpolation
- Matrix manifold
- Parametric model reduction
- Riemannian computing
- Riemannian normal coordinates