Convergence properties of dynamic mode decomposition for analytic interval maps
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929312430555136 |
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| author | Akindji, Elliz Slipantschuk, Julia Bandtlow, Oscar F. Just, Wolfram |
| author_facet | Akindji, Elliz Slipantschuk, Julia Bandtlow, Oscar F. Just, Wolfram |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_08512 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Convergence properties of dynamic mode decomposition for analytic interval maps Akindji, Elliz Slipantschuk, Julia Bandtlow, Oscar F. Just, Wolfram Dynamical Systems 37C30 (Primary) 37E05 (Secondary) 37M10, 37M25, 47A58 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. |
| title | Convergence properties of dynamic mode decomposition for analytic interval maps |
| topic | Dynamical Systems 37C30 (Primary) 37E05 (Secondary) 37M10, 37M25, 47A58 |
| url | https://arxiv.org/abs/2404.08512 |