Singular value decomposition and structures total least norm for approximate greatest common divisor of unvariate polynomials

This study presents experimental works on approximate GCD of univariate polynomials. The computation of approximate GCD is required in the case of imperfectly known or inexact data which emerges from physical measurements or previous computation error. SVD of Sylvester matrix is used to determine th...

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Main Author:	Nordin, Nurul Aida
Format:	Thesis
Language:	English
Published:	2012
Subjects:	Q Science (General)
Online Access:	http://eprints.utm.my/id/eprint/31526/1/NurulAidaNordinMFS2012.pdf
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id	my-utm-ep.31526
record_format	uketd_dc
spelling	my-utm-ep.315262018-04-27T01:16:50Z Singular value decomposition and structures total least norm for approximate greatest common divisor of unvariate polynomials 2012-06 Nordin, Nurul Aida Q Science (General) This study presents experimental works on approximate GCD of univariate polynomials. The computation of approximate GCD is required in the case of imperfectly known or inexact data which emerges from physical measurements or previous computation error. SVD of Sylvester matrix is used to determine the degree of the approximate GCD. Then, STLN method is employed to generate an algorithm for solving the minimization problem that is to find the minimum perturbation such that the perturbed polynomials have a nonconstant GCD. The formulation of the STLN algorithm lead to the formation of LSE problem and this is solved using QR factorization. Every computation is done using MATLAB. Once the minimum perturbation is found, a MATLAB toolbox called Apalab is used to determine the coefficients of the approximate GCD. Results from experimental work performed reveal that the STLN algorithm presented is as efficient as the existing minimization algorithms. 2012-06 Thesis http://eprints.utm.my/id/eprint/31526/ http://eprints.utm.my/id/eprint/31526/1/NurulAidaNordinMFS2012.pdf application/pdf en public masters Universiti Teknologi Malaysia, Faculty of Science Faculty of Science
institution	Universiti Teknologi Malaysia
collection	UTM Institutional Repository
language	English
topic	Q Science (General)
spellingShingle	Q Science (General) Nordin, Nurul Aida Singular value decomposition and structures total least norm for approximate greatest common divisor of unvariate polynomials
description	This study presents experimental works on approximate GCD of univariate polynomials. The computation of approximate GCD is required in the case of imperfectly known or inexact data which emerges from physical measurements or previous computation error. SVD of Sylvester matrix is used to determine the degree of the approximate GCD. Then, STLN method is employed to generate an algorithm for solving the minimization problem that is to find the minimum perturbation such that the perturbed polynomials have a nonconstant GCD. The formulation of the STLN algorithm lead to the formation of LSE problem and this is solved using QR factorization. Every computation is done using MATLAB. Once the minimum perturbation is found, a MATLAB toolbox called Apalab is used to determine the coefficients of the approximate GCD. Results from experimental work performed reveal that the STLN algorithm presented is as efficient as the existing minimization algorithms.
format	Thesis
qualification_level	Master's degree
author	Nordin, Nurul Aida
author_facet	Nordin, Nurul Aida
author_sort	Nordin, Nurul Aida
title	Singular value decomposition and structures total least norm for approximate greatest common divisor of unvariate polynomials
title_short	Singular value decomposition and structures total least norm for approximate greatest common divisor of unvariate polynomials
title_full	Singular value decomposition and structures total least norm for approximate greatest common divisor of unvariate polynomials
title_fullStr	Singular value decomposition and structures total least norm for approximate greatest common divisor of unvariate polynomials
title_full_unstemmed	Singular value decomposition and structures total least norm for approximate greatest common divisor of unvariate polynomials
title_sort	singular value decomposition and structures total least norm for approximate greatest common divisor of unvariate polynomials
granting_institution	Universiti Teknologi Malaysia, Faculty of Science
granting_department	Faculty of Science
publishDate	2012
url	http://eprints.utm.my/id/eprint/31526/1/NurulAidaNordinMFS2012.pdf
_version_	1747815825265393664

Singular value decomposition and structures total least norm for approximate greatest common divisor of unvariate polynomials

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