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Structured matrix methods for computations on Bernstein basis polynomials

Yang, Ning (2013) Structured matrix methods for computations on Bernstein basis polynomials. PhD thesis, University of Sheffield.

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Abstract

This thesis considers structure preserving matrix methods for computations on Bernstein polynomials whose coefficients are corrupted by noise. The ill-posed operations of greatest common divisor computations and polynomial division are considered, and it is shown that structure preserving matrix methods yield excellent results. With respect to greatest common divisor computations, the most difficult part is the computation of its degree, and several methods for its determination are presented. These are based on the Sylvester resultant matrix, and it is shown that a new form of the Sylvester resultant matrix in the modified Bernstein basis yields the best results. The B´ezout resultant matrix in the modified Bernstein basis is also considered, and it is shown that the results from it are inferior to those from the Sylvester resultant matrix in the modified Bernstein basis.

Item Type: Thesis (PhD)
Academic Units: The University of Sheffield > Faculty of Engineering (Sheffield) > Computer Science (Sheffield)
The University of Sheffield > Faculty of Science (Sheffield) > Computer Science (Sheffield)
Identification Number/EthosID: uk.bl.ethos.566363
Depositing User: Mr Ning Yang
Date Deposited: 15 Feb 2013 14:58
Last Modified: 27 Apr 2016 14:11
URI: http://etheses.whiterose.ac.uk/id/eprint/3311

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