Computing Sylvester resultant matrix in hermite polynomials

There has been increasing interest in the theory of polynomials in different fields of science and engineering. Recent work has shown that enhanced numerical solution can be obtained via expressing polynomials in the orthogonal basis such as the Chebyshev, Legendre or Hermite basis. In some problems...

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Main Author:	AlSolami, Somiah Merezeeq A
Format:	Thesis
Language:	English
Published:	2019
Subjects:	QA Mathematics
Online Access:	http://eprints.utm.my/id/eprint/102011/1/AlSomiaSomiahMFS2019.pdf.pdf
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id	my-utm-ep.102011
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spelling	my-utm-ep.1020112023-07-31T06:50:46Z Computing Sylvester resultant matrix in hermite polynomials 2019 AlSolami, Somiah Merezeeq A QA Mathematics There has been increasing interest in the theory of polynomials in different fields of science and engineering. Recent work has shown that enhanced numerical solution can be obtained via expressing polynomials in the orthogonal basis such as the Chebyshev, Legendre or Hermite basis. In some problems, such expression requires transforming resultant matrix between the monomial and the orthogonal or generalized basis. This dissertation concentrates on the possibility of constructing and implementing the Sylvester matrix in the Hermite basis as a computational tool in its orthogonal form. The transformation of the Sylvester resultant matrix between the monomial basis and the orthogonal basis is first studied. The multiplication formulas for some Hermite basis polynomials needed in the computation of the resultant matrix are first derived. Then the computation of the Sylvester resultant matrix in the Hermite basis and the representation of Hermite polynomials with Sylvester type determinants are carried out. The outcomes of this study proved that the Sylvester matrix resultant can be constructed and computed in the Hermite basis. In this form, the matrix can further be applied for working with polynomials in the Hermite basis. Thus. ill-conditioned conversion of polynomials from the orthogonal basis to the monomial basis can be avoided when the input polynomials are represented in the orthogonal basis, in particular the Hermite basis. 2019 Thesis http://eprints.utm.my/id/eprint/102011/ http://eprints.utm.my/id/eprint/102011/1/AlSomiaSomiahMFS2019.pdf.pdf application/pdf en public http://dms.library.utm.my:8080/vital/access/manager/Repository/vital:146261 masters Universiti Teknologi Malaysia Faculty of Science
institution	Universiti Teknologi Malaysia
collection	UTM Institutional Repository
language	English
topic	QA Mathematics
spellingShingle	QA Mathematics AlSolami, Somiah Merezeeq A Computing Sylvester resultant matrix in hermite polynomials
description	There has been increasing interest in the theory of polynomials in different fields of science and engineering. Recent work has shown that enhanced numerical solution can be obtained via expressing polynomials in the orthogonal basis such as the Chebyshev, Legendre or Hermite basis. In some problems, such expression requires transforming resultant matrix between the monomial and the orthogonal or generalized basis. This dissertation concentrates on the possibility of constructing and implementing the Sylvester matrix in the Hermite basis as a computational tool in its orthogonal form. The transformation of the Sylvester resultant matrix between the monomial basis and the orthogonal basis is first studied. The multiplication formulas for some Hermite basis polynomials needed in the computation of the resultant matrix are first derived. Then the computation of the Sylvester resultant matrix in the Hermite basis and the representation of Hermite polynomials with Sylvester type determinants are carried out. The outcomes of this study proved that the Sylvester matrix resultant can be constructed and computed in the Hermite basis. In this form, the matrix can further be applied for working with polynomials in the Hermite basis. Thus. ill-conditioned conversion of polynomials from the orthogonal basis to the monomial basis can be avoided when the input polynomials are represented in the orthogonal basis, in particular the Hermite basis.
format	Thesis
qualification_level	Master's degree
author	AlSolami, Somiah Merezeeq A
author_facet	AlSolami, Somiah Merezeeq A
author_sort	AlSolami, Somiah Merezeeq A
title	Computing Sylvester resultant matrix in hermite polynomials
title_short	Computing Sylvester resultant matrix in hermite polynomials
title_full	Computing Sylvester resultant matrix in hermite polynomials
title_fullStr	Computing Sylvester resultant matrix in hermite polynomials
title_full_unstemmed	Computing Sylvester resultant matrix in hermite polynomials
title_sort	computing sylvester resultant matrix in hermite polynomials
granting_institution	Universiti Teknologi Malaysia
granting_department	Faculty of Science
publishDate	2019
url	http://eprints.utm.my/id/eprint/102011/1/AlSomiaSomiahMFS2019.pdf.pdf
_version_	1776100824728993792

Computing Sylvester resultant matrix in hermite polynomials

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