Preprint No. MPIMD/11-11

Title: Sparse-Dense Sylvester Equations in ℋ₂-Model Order Reduction

Author(s): Peter Benner, Martin Köhler, Jens Saak


Date: 2011-12-16


In this paper we study the pratical implementation of a new algorithm for H₂-model order reduction, the so called two sided iteration algorithm (TSIA). It is based on the work of Wilson from 1970 and the extensions done by Xu and Zeng. The main idea behind this algorithm is to fulfill a classical first order optimality condition. Other approaches for H₂-model order reduction are for example the IRKA algorithm which is based on the interpolation of the transfer function. The theoretical connection between both ideas is verified and the numerical behavior of both approaches is compared. An adaption for generalized state space systems is done, too. In order to implement the presented algorithm robustly and efficiently, it is crucial to overcome some numerical and technical problems. We present a new idea to compute the oblique projection and a fast solver for the Sylvester equation. The benefits of the algorithmic improvements presented in this paper are illustrated by several numerical examples.


author = {Peter Benner and Martin Köhler and Jens Saak},
title = {Sparse-Dense Sylvester Equations in ℋ₂-Model Order Reduction},
number = {MPIMD/11-11},
month = dec,
year = 2011,
institution = {Max Planck Institute Magdeburg},
type = {Preprint},
note = {Available from \url{}},

Download MPIMD/11-11