Interpolatory $\mathcal{H}_{\infty}$ Model Reduction

Details Interpolatory $\mathcal{H}_{\infty}$ Model Reduction Interpolatory $\mathcal{H}_{\infty}$ Model Reduction

2011-07-27

arxiv.org/abs/1107.5364v1

Mathematics

Numerical Analysis

Scientific paper

We introduce an interpolation framework for $\mathcal{H}_{\infty}$ model reduction founded on ideas from optimal-$\mathcal{H}_2$ interpolatory model reduction, realization theory, and complex Chebyshev approximation. We propose a method that can be applied effectively in large-scale settings with the main cost being (typically) sparse linear solves. Several numerical examples illustrate that our approach will produce high fidelity reduced-order models that consistently exhibit better $\mathcal{H}_{\infty}$ performance than those produced by balanced truncation. Often they are as good as (and occasionally better than) those produced by optimal Hankel norm approximation; and in all cases these reduced models can be produced at far lower cost.

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