{"ID":2892396,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.15837","arxiv_id":"2507.15837","title":"Data-driven optimal approximation on Hardy spaces in simply connected domains","abstract":"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.","short_abstract":"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...","url_abs":"https://arxiv.org/abs/2507.15837","url_pdf":"https://arxiv.org/pdf/2507.15837v1","authors":"[\"Alessandro Borghi\",\"Tobias Breiten\"]","published":"2025-07-21T17:47:44Z","proceeding":"math.NA","tasks":"[\"math.NA\",\"math.OC\"]","methods":"[]","has_code":false}