A Unified Algebraic Framework for Subspace Pruning in Koopman Operator Approximation via Principal Vectors
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866917371968487424 |
|---|---|
| author | Shah, Dhruv Cortes, Jorge |
| author_facet | Shah, Dhruv Cortes, Jorge |
| contents | Finite-dimensional approximations of the Koopman operator rely critically on identifying nearly invariant subspaces. This invariance proximity can be rigorously quantified via the principal angles between a candidate subspace and its image under the operator. To systematically minimize this error, we propose an algebraic framework for subspace pruning utilizing principal vectors. We establish the equivalence of this approach to existing consistency-based methods while providing a foundation for broader generalizations. To ensure scalability, we introduce an efficient numerical update scheme based on rank-one modifications, reducing the computational complexity of tracking principal angles by an order of magnitude. Finally, we demonstrate the effectiveness of our framework through numerical simulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_29001 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Unified Algebraic Framework for Subspace Pruning in Koopman Operator Approximation via Principal Vectors Shah, Dhruv Cortes, Jorge Systems and Control Finite-dimensional approximations of the Koopman operator rely critically on identifying nearly invariant subspaces. This invariance proximity can be rigorously quantified via the principal angles between a candidate subspace and its image under the operator. To systematically minimize this error, we propose an algebraic framework for subspace pruning utilizing principal vectors. We establish the equivalence of this approach to existing consistency-based methods while providing a foundation for broader generalizations. To ensure scalability, we introduce an efficient numerical update scheme based on rank-one modifications, reducing the computational complexity of tracking principal angles by an order of magnitude. Finally, we demonstrate the effectiveness of our framework through numerical simulations. |
| title | A Unified Algebraic Framework for Subspace Pruning in Koopman Operator Approximation via Principal Vectors |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2603.29001 |