Model Reduction by Rational Interpolation

TL;DR

This paper surveys recent advances in interpolatory model reduction techniques for large-scale linear dynamical systems, highlighting methods for optimal, measurement-based, parametrized, weighted, and structure-preserving reductions.

Contribution

It provides a comprehensive overview of interpolatory model reduction methods, including recent developments and numerical examples, from basic principles to advanced topics.

Findings

Recent methods enable locally optimal reduced models at modest computational cost.

Extensions allow reduction directly from input/output measurements.

Numerical examples illustrate effectiveness of various interpolatory techniques.

Abstract

The last two decades have seen major developments in interpolatory methods for model reduction of large-scale linear dynamical systems. Advances of note include the ability to produce (locally) optimal reduced models at modest cost; refined methods for deriving interpolatory reduced models directly from input/output measurements; and extensions for the reduction of parametrized systems. This chapter offers a survey of interpolatory model reduction methods starting from basic principles and ranging up through recent developments that include weighted model reduction and structure-preserving methods based on generalized coprime representations. Our discussion is supported by an assortment of numerical examples.