  We introduce an interpolation framework for H-infinity model reduction
founded on ideas originating in optimal-H2 interpolatory model reduction,
realization theory, and complex Chebyshev approximation. By employing a Loewner
"data-driven" framework within each optimization cycle, large-scale H-infinity
norm calculations can be completely avoided. Thus, we are able to formulate a
method that remains effective in large-scale settings with the main cost
dominated by sparse linear solves. Several numerical examples illustrate that
our approach will produce high fidelity reduced models consistently exhibiting
better H-infinity 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, these reduced
models are produced at far lower cost than is possible either with balanced
truncation or optimal Hankel norm approximation.
