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Convergence properties of dynamic mode decomposition for analytic interval maps

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arxiv 2404.08512 v1 pith:LF4VPLQA submitted 2024-04-12 math.DS

Elliz Akindji , Julia Slipantschuk , Oscar F. Bandtlow , Wolfram Just This is my paper · ORCID
classification math.DS
keywords convergencemethodspectralanalyticdecompositiondynamicedmdinterval
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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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  1. Avoiding spectral pollution for transfer operators using residuals

    math.DS 2025-07 conditional novelty 6.0 of 10

    A residual computation for kernelized dynamic mode decomposition gives a necessary condition for eigenvalues of transfer operators, enabling detection of spectral pollution.

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