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- W4225773934 abstract "We study numerical approaches to computation of spectral properties of composition operators. We provide a characterization of Koopman Modes in Banach spaces using Generalized Laplace Analysis. We cast the Dynamic Mode Decomposition-type methods in the context of Finite Section theory of infinite dimensional operators, and provide an example of a mixing map for which the finite section method fails. Under assumptions on the underlying dynamics, we provide the first result on the convergence rate under sample size increase in the finite-section approximation. We study the error in the Krylov subspace version of the finite section method and prove convergence in pseudospectral sense for operators with pure point spectrum. Since Krylov sequence-based approximations can mitigate the curse of dimensionality, this result indicates that they may also have low spectral error without an exponential-in-dimension increase in the number of functions needed." @default.
- W4225773934 created "2022-05-05" @default.
- W4225773934 creator A5014334832 @default.
- W4225773934 date "2022-04-05" @default.
- W4225773934 modified "2023-10-09" @default.
- W4225773934 title "On Numerical Approximations of the Koopman Operator" @default.
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- W4225773934 doi "https://doi.org/10.3390/math10071180" @default.
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