THE GENERAL RATIONAL INTERPOLATION PROBLEM IN THE SCALAR CASE AND ITSHANKEL VECTOR

This paper deals with the general rational interpolation problem (GRIP ) in the scalar case. In the recent work of Antoulas, Ball, gang, and Willems the general solution to the GRIP has been derived in the frame work 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 x 2 polynomial generating mat rix, based on the deep connection between Loewner and Hankel matrices. If turns out that given a fixed GRIP, we can readily obtain a unique vector, called the Hankel vector, such that both of the allowable McMi llan degrees of interpolants to this GRIP and the corresponding polyno mial generating matrix are completely determined by this Hankel vector combined with its characteristic degrees and characteristic polynomia ls.