Data-driven optimal approximation on Hardy spaces in simply connected domains
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911068085813248 |
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| author | Borghi, Alessandro Breiten, Tobias |
| author_facet | Borghi, Alessandro Breiten, Tobias |
| contents | We consider optimal interpolation of functions analytic in simply connected domains in the complex plane. By choosing a specific structure for the approximant, we show that the resulting first order optimality conditions can be interpreted as optimal $\mathcal{H}_2$ interpolation conditions for discrete-time dynamical systems. Connections to the implicit Euler method, the midpoint method, and backward differentiation methods are also established. A data-driven algorithm is developed to compute a (locally) optimal approximant. Our method is tested on three numerical experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_15837 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Data-driven optimal approximation on Hardy spaces in simply connected domains Borghi, Alessandro Breiten, Tobias Numerical Analysis Optimization and Control We consider optimal interpolation of functions analytic in simply connected domains in the complex plane. By choosing a specific structure for the approximant, we show that the resulting first order optimality conditions can be interpreted as optimal $\mathcal{H}_2$ interpolation conditions for discrete-time dynamical systems. Connections to the implicit Euler method, the midpoint method, and backward differentiation methods are also established. A data-driven algorithm is developed to compute a (locally) optimal approximant. Our method is tested on three numerical experiments. |
| title | Data-driven optimal approximation on Hardy spaces in simply connected domains |
| topic | Numerical Analysis Optimization and Control |
| url | https://arxiv.org/abs/2507.15837 |