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arXiv · 2404.08512

Convergence properties of dynamic mode decomposition for analytic interval maps

Elliz Akindji·Julia Slipantschuk·Oscar F. Bandtlow·Wolfram Just
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Abstract

Extended dynamic mode decomposition (EDMD) is a data-driven algorithm for approximating spectral data of the Koopman operator associated to a dynamical system, combining a Galerkin method of order N and collocation method of order M. Spectral convergence of this method subtly depends on appropriate choice of the space of observables. For chaotic analytic full branch maps of the interval, we derive a constraint between M and N guaranteeing spectral convergence of EDMD.

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Elliz Akindji, Julia Slipantschuk, Oscar F. Bandtlow, Wolfram Just. 2024-04-12. Convergence properties of dynamic mode decomposition for analytic interval maps. https://arxiv.org/abs/2404.08512

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