A Restart Scheme for Model Order Reduction Using the Iterative Rational Krylov Algorithm

Abstract

We propose a restart scheme for the iterative rational Krylov algorithm (IRKA) in order to ensure higher order moment matching in the model reduction scheme. The IRKA method is well-used in the literature for reduction of linear systems as it satisfies the necessary conditions for H2 optimality. Recently, IRKA method has been extended to model reduction of descriptive systems as well as non linear systems. The reduced models obtained through IRKA ensure hermite interpolations. However, higher order moments are not matched by the IRKA method. In this work, we show that the basis matrices can be constructed through repeated use of IRKA with some modifications of the input matrices in each repetition. The Petrov-Galerkin projection with the basis matrices results in a reduced model that ensures higher order moment matching in addition to hermite interpolation and give better H2 norm error as compared to IRKA, in some cases. An important future work will be the extension of restart IRKA to descriptor systems