Convergence properties of dynamic mode decomposition for analytic interval maps

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 functions and a quadrature method with 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 and guaranteeing spectral convergence of EDMD. In particular, the computed eigenvalues converge exponentially fast (in ) to the eigenvalues of the Koopman operator, taken to act on the dual space of a certain Banach space of analytic functions.