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Krylov subspaces associated with higher-order linear dynamical systems
Roland W. Freund, University of California, Davis
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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.
SUGGESTED CITATION:
REQUIRED PUBLISHER STATEMENT:
Roland W. Freund,
"Krylov subspaces associated with higher-order linear dynamical systems"
(2005).
Bit Numerical Mathematics.
45 (3),
pp. 495-516.
Postprint available free at: http://repositories.cdlib.org/postprints/1449
The original publication is available at www.springerlink.com in Bit Numerical Mathematics.
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