A Unifying Framework for Interpolatory \({\boldsymbol{\mathcal{L}_2}}\)-Optimal Reduced-Order Modeling.

We develop a unifying framework for interpolatory -optimal reduced-order modeling for a wide class 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 -optimal model order reduction and leads to the interpolatory conditions for -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 -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 in two numerical examples.