Krylov subspaces associated with higher-order linear dynamical systems
Abstract
A standard approach to model reduction of large-scale higher-order linear dynamical systems is to rewrite the system as an equivalent first-order system and then employ Krylov-subspace techniques for model reduction of first-order systems. This paper presents some results about the structure of the block-Krylov subspaces induced by the matrices of such equivalent first-order formulations of higher-order systems. Two general classes of matrices, which exhibit the key structures of the matrices of first-order formulations of higher-order systems, are introduced. It is proved that for both classes, the block-Krylov subspaces induced by the matrices in these classes can be viewed as multiple copies of certain subspaces of the state space of the original higher-order system.
Keywords
Cite
@article{arxiv.math/0501484,
title = {Krylov subspaces associated with higher-order linear dynamical systems},
author = {Roland W. Freund},
journal= {arXiv preprint arXiv:math/0501484},
year = {2007}
}