A Unifying Framework for Interpolatory ℒ_2-optimal Reduced-order Modeling

09/01/2022

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by   Petar Mlinarić, et al.

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We develop a unifying framework for interpolatory ℒ_2-optimal reduced-order modeling for a wide classes of problems ranging from stationary models to parametric dynamical systems. We first show that the framework naturally covers the well-known interpolatory necessary conditions for ℋ_2-optimal model order reduction and leads to the interpolatory conditions for ℋ_2 ⊗ℒ_2-optimal model order reduction of multi-input/multi-output parametric dynamical systems. Moreover, we derive novel interpolatory optimality conditions for rational discrete least-squares minimization and for ℒ_2-optimal model order reduction of a class of parametric stationary models. We show that bitangential Hermite interpolation appears as the main tool for optimality across different domains. The theoretical results are illustrated on two numerical examples.