A note on matrix-valued rational interpolants

Fraction-Free Computation of Matrix Rational Interpolants and Matrix GCDs

We present a new set of algorithms for computation of matrix rational interpolants and one-sided matrix greatest common divisors. Examples of these interpolants include Padé approximants, Newton–Padé, Hermite–Padé, and simultaneous Padé approximants, and more generally M-Padé approximants along with their matrix generalizations. The algorithms are fast and compute all solutions to a given probl...

Algebraic properties of some new vector-valued rational interpolants

In a recent paper of the author [A. Sidi,A new approach to vector-valued rational interpolation, J.Approx. Theory, 130 (2004) 177–187], three new interpolation procedures for vector-valued functions F(z), where F : C → CN , were proposed, and some of their properties were studied. In this work, after modifying their definition slightly, we continue the study of these interpolation procedures. W...

Convergence of Rational Interpolants∗

The convergence of (diagonal) sequences of rational interpolants to an analytic function is investigated. Problems connected with their definition are shortly discussed. Results about locally uniform convergence are reviewed. Then the convergence in capacity is studied in more detail. Here, a central place is taken by a theorem about the convergence in capacity of rational interpolants to funct...

Vector Fitting for Matrix-valued Rational Approximation

Vector Fitting (VF) is a popular method of constructing rational approximants that provides a least squares fit to frequency response measurements. In an earlier work, we provided an analysis of VF for scalar-valued rational functions and established a connection with optimal H 2 approximation. We build on this work and extend the previous framework to include the construction of effective rati...

On the differential structure of matrix–valued rational inner functions