A model reduction method in large scale dynamical systems using an extended-rational block Arnoldi method

Abstract

In this paper, we propose a new block Krylov-type subspace method for model reduction in large scale dynamical systems. We project the initial problem onto a new subspace, generated as a combination of rational and polynomial block Krylov subspaces. Simple algebraic properties are given and expressions of the error between the original and reduced transfer functions are established. Furthermore, we present an adaptive strategy of the interpolation points that will be used in the construction of our new block Krylov subspace. We also show how this method can be used to extract an approximate low rank solution of large-scale Lyapunov equations. Numerical results are reported on some benchmark examples to confirm the performance of our method compared with other known methods.