Model Reduction by Rational Interpolation

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. Mathematics Subject Classification (2010). 41A05, 93A15, 93C05, 37M99.