Realization-independent H 2-approximation

Iterative Rational Krylov Algorithm (IRKA) of [11] is an effective tool for tackling the H2-optimal model reduction problem. However, so far it has relied on a first-order state-space realization of the model-to-be-reduced. In this paper, by exploiting the Loewner-matrix approach for interpolation, we develop a new formulation of IRKA that only requires transfer function evaluations without access to any particular realization. This, in turn, extends IRKA to H2 approximation of irrational, infinite-dimensional dynamical systems. We also introduce a residue-correction step in IRKA that adjusts the vector residues to minimize the H2 error at the end of each cycle using a new set of necessary and sufficient conditions for H2 optimality. This new step further improves the convergence speed and performance of IRKA. Three numerical examples illustrate the effectiveness of the proposed methods.

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