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A non-linear structure preserving matrix method for the low rank approximation of the Sylvester resultant matrix

Winkler, J.R. and Hasan, M. (2010) A non-linear structure preserving matrix method for the low rank approximation of the Sylvester resultant matrix. Journal of Computational and Applied Mathematics, 234 (12). pp. 3226-3242. ISSN 0377-0427

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Abstract

A non-linear structure preserving matrix method for the computation of a structured low rank approximation S((f) over bar , (g) over bar) of the Sylvester resultant matrix S(f , g) of two inexact polynomials f = f(y) and g = g(y) is considered in this paper. It is shown that considerably improved results are obtained when f (y) and g(y) are processed prior to the computation of S((f) over bar , (g) over bar), and that these preprocessing operations introduce two parameters. These parameters can either be held constant during the computation of S((f) over bar , (g) over bar), which leads to a linear structure preserving matrix method, or they can be incremented during the computation of S((f) over bar, (g) over bar), which leads to a non-linear structure preserving matrix method. It is shown that the non-linear method yields a better structured low rank approximation of S((f) over bar , (g) over bar) and that the assignment of f (y) and g(y) is important because S((f) over bar , (g) over bar) may be a good structured low rank approximation of S(f, g), but S((f) over bar , (g) over bar) may be a poor structured low rank approximation of S (g f) because its numerical rank is not defined. Examples that illustrate the differences between the linear and non-linear structure preserving matrix methods, and the importance of the assignment off (y) and g(y), are shown. (C) 2010 Elsevier B.V. All rights reserved.

Item Type: Article
Copyright, Publisher and Additional Information: © 2010 Elsevier. This is an author produced version of a paper subsequently published in Journal of Computational and Applied Mathematics. Uploaded in accordance with the publisher's self-archiving policy.
Keywords: Sylvester matrix; Structured low rank approximation
Academic Units: The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Computer Science (Sheffield)
Depositing User: Miss Anthea Tucker
Date Deposited: 10 Sep 2010 14:47
Last Modified: 08 Feb 2013 17:01
Published Version: http://dx.doi.org/10.1016/j.cam.2010.04.013
Status: Published
Publisher: Elsevier
Refereed: Yes
Identification Number: 10.1016/j.cam.2010.04.013
URI: http://eprints.whiterose.ac.uk/id/eprint/11215

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