A Unifying Framework for Interpolatory -optimal Reduced-order Modeling
arXiv:2209.00714 · doi:10.1137/22M1516920
Abstract
We develop a unifying framework for interpolatory -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 -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 on two numerical examples.
arXiv comment20 pages, 2 figures
References in corpus (13)
- The AAA algorithm for rational approximation
- Structure-preserving tangential interpolation for model reduction of port-Hamiltonian Systems
- Model Reduction of Descriptor Systems by Interpolatory Projection Methods
- Quadrature-Based Vector Fitting: Implications For H2 System Approximation
- Multipoint Volterra Series Interpolation and H2 Optimal Model Reduction of Bilinear Systems
- Interpolatory Weighted-H2 Model Reduction
- Vector Fitting for Matrix-valued Rational Approximation
- Near-optimal Frequency-weighted Interpolatory Model Reduction
- Interpolatory H-infinity Model Reduction
- On Error Estimation for Reduced-order Modeling of Linear Non-parametric and Parametric Systems
- Structure-Preserving Interpolation of Bilinear Control Systems
- Structure-Preserving Interpolation for Model Reduction of Parametric Bilinear Systems
- -Optimal Model Reduction Using Projected Nonlinear Least Squares