Preprint des Projektes: SFB 701: Spektrale Strukturen und Topologische Methoden in der Mathematik - Projekt B3

Numerische Analyse äquivarianter Evolutionsgleichungen

10-048 Jens Kemper.
Long-time behavior of the POD method

We present explicit error bounds concerning the behavior of the proper orthogonal decomposition (POD) method when the data is drawn from long trajectories. We express the error of the POD method in terms of the canonical angle for systems with exponentially decaying behavior. We test our theoretical bounds numerically using a linear parabolic equation. The considerations are motivated by a subdivision algorithm for the computation of invariant measures in discrete dynamical systems using the POD method as a model reduction tool.