Long‐time behavior of the proper orthogonal decomposition method
Copyright policy )Long‐time behavior of the proper orthogonal decomposition method
SUMMARYWe present explicit error bounds concerning the behavior of the proper orthogonal decomposition (POD) method when the data are 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. Copyright © 2011 John Wiley & Sons, Ltd.
- Bielefeld University Germany
Numerical optimization and variational techniques, infinite horizon problem, Eigenvalues, singular values, and eigenvectors, singular value decomposition, eigenvalues, System structure simplification, error estimate, Feedback control, dynamical system, proper orthogonal decomposition, evolution problem, model reduction, feedback synthesis, Initial-boundary value problems for second-order parabolic systems, perturbation analysis, numerical experiments, Control/observation systems governed by ordinary differential equations
Numerical optimization and variational techniques, infinite horizon problem, Eigenvalues, singular values, and eigenvectors, singular value decomposition, eigenvalues, System structure simplification, error estimate, Feedback control, dynamical system, proper orthogonal decomposition, evolution problem, model reduction, feedback synthesis, Initial-boundary value problems for second-order parabolic systems, perturbation analysis, numerical experiments, Control/observation systems governed by ordinary differential equations
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