In this paper we review the state of affairs in the area of approximation of large-scale systems. We distinguish among three basic categories, namely the SVD-based, the Krylov-based and theâ€¦ (More)

The optimal H2 model reduction problem is of great importance in the area of dynamical systems and simulation. In the literature, two independent frameworks have evolved focussing either on solutionâ€¦ (More)

An overview of model reduction methods and a comparison of the resulting algorithms is presented. These approaches are divided into two broad categories, namely SVD based and moment matching basedâ€¦ (More)

This paper addresses the problem of modeling systems from measurements of their frequency response. For multiport devices, currently available techniques are expensive. We propose a new approachâ€¦ (More)

This paper investigates the decay rate of the Hankel singular values of linear dynamical systems. This issue is of considerable interest in model reduction by means of balanced truncation, forâ€¦ (More)

Approximation is an important issue in the theory and practice of dynamical systems. In this essay we will review a theory of approximation of linear dynamical systems which has two importantâ€¦ (More)

We develop and describe an iteratively corrected rational Krylov algorithm for the solution of the optimal H2 model reduction problem. The formulation is based on finding a reduced order model thatâ€¦ (More)

In this note we present a modified cyclic low-rank Smith method to compute low-rank approximations to solutions of Lyapunov equations arising from large-scale dynamical systems. Unlike the originalâ€¦ (More)