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 ${\mathcal{H}}_2$ approximation. We build on this work and extend the previous framework to include the construction of effective rational approximations to matrix-valued functions, a problem which presents significant challenges that do not appear in the scalar case. Transfer functions associated with multi-input/multioutput (MIMO) dynamical systems typify the class of functions that we consider here. Others have also considered extensions of VF to matrix-valued functions and related numerical implementations are readily available. However, to the best of our knowledge, a detailed analysis of numerical issues that arise does not yet exist. We offer such an analysis including critical implementation details here. One important issue t...

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