Convergence properties of dynamic mode decomposition for analytic interval maps

Titelangaben

Akindji, Elliz ; Slipantschuk, Julia ; Bandtlow, Oscar F. ; Just, Wolfram:
Convergence properties of dynamic mode decomposition for analytic interval maps.
In: Communications on Pure and Applied Mathematics. Bd. 79 (2026) Heft 2 . - S. 179-206.
ISSN 1097-0312
DOI: https://doi.org/10.1002/cpa.70011

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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 with N functions and a quadrature method with M quadrature nodes. Spectral convergence of this method subtly depends on an 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. In particular, the computed eigenvalues converge exponentially fast (in N) to the eigenvalues of the Koopman operator, taken to act on the dual space of a certain Banach space of analytic functions.