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Structured total least norm and approximate GCDs of inexact polynomials

Winkler, J.R. and Allan, J.D. (2008) Structured total least norm and approximate GCDs of inexact polynomials. Journal of Computational and Applied Mathematics, 215 (1). pp. 1-13. ISSN 0377-0427


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The determination of an approximate greatest common divisor (GCD) of two inexact polynomials f=f(y) and g=g(y) arises in several applications, including signal processing and control. This approximate GCD can be obtained by computing a structured low rank approximation S*(f,g) of the Sylvester resultant matrix S(f,g). In this paper, the method of structured total least norm (STLN) is used to compute a low rank approximation of S(f,g), and it is shown that important issues that have a considerable effect on the approximate GCD have not been considered. For example, the established works only yield one matrix S*(f,g), and therefore one approximate GCD, but it is shown in this paper that a family of structured low rank approximations can be computed, each member of which yields a different approximate GCD. Examples that illustrate the importance of these and other issues are presented.

Item Type: Article
Copyright, Publisher and Additional Information: © 2008 Elsevier B.V. This is an author produced version of a paper published in Journal of Computational and Applied Mathematics. Uploaded in accordance with the publisher's self-archiving policy.
Institution: The University of Sheffield
Academic Units: The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Computer Science (Sheffield)
Depositing User: Sherpa Assistant
Date Deposited: 02 May 2008 11:02
Last Modified: 06 Jun 2014 10:03
Published Version: http://dx.doi.org/10.1016/j.cam.2007.03.018
Status: Published
Publisher: Elsevier Science BV
Identification Number: 10.1016/j.cam.2007.03.018
URI: http://eprints.whiterose.ac.uk/id/eprint/3768

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