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.
Interpolatory Approximations of PMU Data: Dimension Reduction and Pilot Selection
Courant Institute of Mathematical Sciences, New York University（纽约大学柯朗数学科学研究所）；Department of Mathematics, Virginia Tech（弗吉尼亚理工大学数学系）；Elmore Family School of Electrical and Computer Engineering, Purdue University（普渡大学埃尔莫电气与计算机工程学院）
$\mathcal{H}_2$-optimal model reduction of linear quadratic-output systems by multivariate rational interpolation
Courant Institute of Mathematical Sciences, New York University（纽约大学库朗数学科学研究所）；Max Planck Institute for Dynamics of Complex Technical Systems（马克斯·普朗克复杂技术系统动力学研究所）；Virginia Tech（弗吉尼亚理工大学）
Low-Rank Matrix Approximation in the Infinity Norm
Department of Mathematics and Operational Research, University of Mons（蒙斯大学数学与运筹学系）；National Research University Higher School of Economics（俄罗斯国家研究大学高等经济学院）
