Data-driven optimal approximation on Hardy spaces in simply connected domains
Numerical Analysis
2025-07-22 v1 Numerical Analysis
Optimization and Control
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 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.
Cite
@article{arxiv.2507.15837,
title = {Data-driven optimal approximation on Hardy spaces in simply connected domains},
author = {Alessandro Borghi and Tobias Breiten},
journal= {arXiv preprint arXiv:2507.15837},
year = {2025}
}