Data‐driven approximation methods applied to non‐rational functions. Issue 1 (17th December 2018) - Karachalios, Dimitrios S.; Gosea, Ion Victor; Antoulas, Athanasios C.
Abstract: In this study, four data‐driven interpolation‐based methods are compared. The aim is to construct reduced‐order models for which the corresponding rational transfer function matches the original non‐rational one at selected interpolation points. The primary method of this study is the Loewner framework [2] which addresses this problem in a natural and direct way. The other methods that were studied, vector fitting (VF) [5], and adaptive Antoulas‐Anderson (AAA) [4], are instead based on an iterative and adaptive selection procedure. In order to present the adaptive selection as a feature in the Loewner framework and to reduce the time complexity at the same time, we introduced a Loewner CUR method based on the cross approximation algorithm [6, 7]. The performance of the above methods is tested by a classical example in approximation theory: the inverse of the Bessel function of the first kind.