The general rational interpolation problem in the scalar case and its Hankel vector

Abstract

This paper deals with the general rational interpolation problem (GRIP) in the scalar case. In the recent work of Antoulas, Ball, Kang, and Willems the general solution to the GRIP has been derived in the framework of linear fractions using the so-called generating matrix as the main tool. Within this framework, the contribution here consists in a new approach of computing a particular 2 × 2 polynomial generating matrix, based on the deep connection between Loewner and Hankel matrices. It turns out that given a fixed GRIP, we can readily obtain a unique vector, called the Hankel vector, such that both of the allowable McMillan degrees of interpolants to this GRIP and the corresponding polynomial generating matrix are completely determined by this Hankel vector combined with its characteristic degrees and characteristic polynomials.