Realization-independent ℌ2-approximation

The Iterative Rational Krylov Algorithm (IRKA) of [9] is an effective tool for approaching the H
₂
-optimal model reduction problem. However, it has relied on the availability of a standard first-order state-space realization of the model-to-be-reduced. In this paper, we employ a Loewner-matrix approach for interpolation, and develop a new formulation of IRKA that only uses transfer function evaluations, without requiring any particular realization. This allows extension of IRKA to H
₂
approximation of irrational, infinite-dimensional dynamical systems. We incorporate a residue-correction step within IRKA that adjusts vector residues so as to minimize the H
₂
error at the end of each cycle. Two numerical examples illustrate the effectiveness of the proposed methods.