Interpolatory model reduction

We introduce an approach to H ∞ model reduction that is founded on ideas originating in realization theory, interpolatory H 2 -optimal model reduction, and complex Chebyshev approximation. Within this new framework, we are able to formulate a method that remains effective in large-scale settings with the main cost dominated by sparse linear solves. By employing Loewner “data-driven” partial realizations within each optimization cycle, computationally demanding H ∞ norm calculations can be completely avoided. Several numerical examples illustrate that our approach will produce high fidelity reduced models consistently exhibiting better H ∞ performance than those produced by balanced truncation; these models often are as good as (and occasionally better than) those models produced by optimal Hankel norm approximation. In all cases, reduced models are produced at far lower cost than is possible either with balanced truncation or with optimal Hankel norm approximation.