Preprint of the project:
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.
