Data-driven optimal approximation on Hardy spaces in simply connected domains

Alessandro Borghi; Tobias Breiten

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arXiv · 2507.15837

Data-driven optimal approximation on Hardy spaces in simply connected domains

Alessandro Borghi·Tobias Breiten

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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.

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Alessandro Borghi, Tobias Breiten. 2025-07-21. Data-driven optimal approximation on Hardy spaces in simply connected domains. https://arxiv.org/abs/2507.15837

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