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 H2 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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