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Padé-Type Model Reduction of Second-Order and Higher-Order Linear Dynamical Systems

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Dimension Reduction of Large-Scale Systems

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 45))

Summary

A standard approach to reduced-order modeling of higher-order linear dynamical systems is to rewrite the system as an equivalent first-order system and then employ Krylov-subspace techniques for reduced-order modeling of first-order systems. While this approach results in reduced-order models that are characterized as Padé-type or even true Padé approximants of the system's transfer function, in general, these models do not preserve the form of the original higher-order system. In this paper, we present a new approach to reduced-order modeling of higher-order systems based on projections onto suitably partitioned Krylov basis matrices that are obtained by applying Krylov-subspace techniques to an equivalent first-order system. We show that the resulting reduced-order models preserve the form of the original higher-order system. While the resulting reduced-order models are no longer optimal in the Padé sense, we show that they still satisfy a Padé-type approximation property. We also introduce the notion of Hermitian higher-order linear dynamical systems, and we establish an enhanced Padé-type approximation property in the Hermitian case.

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Authors and Affiliations

  1. Department of Mathematics, University of California at Davis, One Shields Avenue, Davis, CA, 95616, USA

    Roland W. Freund

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  1. Roland W. Freund
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Editor information

Editors and Affiliations

  1. Fakultät für Mathematik, Technische Universität Chemnitz, 09107, Chemnitz, Germany

    Peter Benner

  2. Department of Computational and Applied Mathematics, Rice University, Main Street 6100, 77005-1892, Houston, TX, USA

    Danny C. Sorensen

  3. Institut für Mathematik, Technische Universität Berlin, Straße des 17. Juni 136, 10623, Berlin, Germany

    Volker Mehrmann

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© 2005 Springer-Verlag Berlin Heidelberg

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Freund, R.W. (2005). Padé-Type Model Reduction of Second-Order and Higher-Order Linear Dynamical Systems. In: Benner, P., Sorensen, D.C., Mehrmann, V. (eds) Dimension Reduction of Large-Scale Systems. Lecture Notes in Computational Science and Engineering, vol 45. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-27909-1_8

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