7 Manifold interpolation

Abstract

One approach to parametric and adaptive model reduction is via the interpolation<br/>of orthogonal bases, subspaces or positive definite system matrices. In all<br/>these cases, the sampled inputs stem from matrix sets that feature a geometric structure<br/>and thus form so-called matrix manifolds. This chapter reviews the numerical<br/>treatment of the most important matrix manifolds that arise in the context of model<br/>reduction. Moreover, the principal approaches to data interpolation and Taylor-like<br/>extrapolation on matrix manifolds are outlined and complemented by algorithms in<br/>pseudo-code.

Topics & Concepts