Algorithms for the Rational Approximation of Matrix-Valued Functions

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

Dual Szegö pairs of sequences of rational matrix-valued functions

We study certain sequences of rational matrix-valued functions with poles outside the unit circle. These sequences are recursively constructed based on a sequence of complex numbers with norm less than one and a sequence of strictly contractive matrices. We present some basic facts on the rational matrix-valued functions belonging to such kind of sequences and we will see that the validity of s...

The best uniform polynomial approximation of two classes of rational functions

In this paper we obtain the explicit form of the best uniform polynomial approximations out of Pn of two classes of rational functions using properties of Chebyshev polynomials. In this way we present some new theorems and lemmas. Some examples will be given to support the results.

Approximation by Rational Functions