Realization-independent ℌ2-approximation

The Iterative Rational Krylov Algorithm (IRKA) of [9] is an effective tool for approaching the H2-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 H2 approximation of irrational, infinite-dimensional dynamical systems. We incorporate a residue-correction step within IRKA that adjusts vector residues so as to minimize the H2 error at the end of each cycle. Two numerical examples illustrate the effectiveness of the proposed methods.

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