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
Abstract
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.
Metadata
Item Type: | Article |
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Authors/Creators: |
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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. |
Dates: |
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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 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:3768 |