Polynomial degree reduction in the L2-norm on a symmetric interval for the canonical basis

In this paper, we develop a direct formula for determining the coefficients in the canonical basis of the best polynomial of degree M that approximates a polynomial of degree N>Mon a symmetric interval for the L2-norm. We also formally prove that using the formula is more computationally efficien...

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Main Authors:	Habib Ben Abdallah, Christopher J. Henry, Sheela Ramanna
Format:	Article
Language:	English
Published:	Elsevier 2021-11-01
Series:	Results in Applied Mathematics
Subjects:	Polynomial degree reduction Legendre polynomials Optimization Euclidian norm Canonical basis
Online Access:	http://www.sciencedirect.com/science/article/pii/S2590037421000352

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record_format	Article
spelling	doaj-c72dae880a4445fea77472f7372ac40e2021-09-24T09:49:44ZengElsevierResults in Applied Mathematics2590-03742021-11-0112100185Polynomial degree reduction in the L2-norm on a symmetric interval for the canonical basisHabib Ben Abdallah0Christopher J. Henry1Sheela Ramanna2Corresponding author.; Department of Applied Computer Science, University of Winnipeg, Winnipeg, Manitoba, CanadaDepartment of Applied Computer Science, University of Winnipeg, Winnipeg, Manitoba, CanadaDepartment of Applied Computer Science, University of Winnipeg, Winnipeg, Manitoba, CanadaIn this paper, we develop a direct formula for determining the coefficients in the canonical basis of the best polynomial of degree M that approximates a polynomial of degree N>Mon a symmetric interval for the L2-norm. We also formally prove that using the formula is more computationally efficient than using a classical matrix multiplication approach and we provide an example to illustrate that it is more numerically stable than the classical approach.http://www.sciencedirect.com/science/article/pii/S2590037421000352Polynomial degree reductionLegendre polynomialsOptimizationEuclidian normCanonical basis
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Habib Ben Abdallah Christopher J. Henry Sheela Ramanna
spellingShingle	Habib Ben Abdallah Christopher J. Henry Sheela Ramanna Polynomial degree reduction in the L2-norm on a symmetric interval for the canonical basis Results in Applied Mathematics Polynomial degree reduction Legendre polynomials Optimization Euclidian norm Canonical basis
author_facet	Habib Ben Abdallah Christopher J. Henry Sheela Ramanna
author_sort	Habib Ben Abdallah
title	Polynomial degree reduction in the L2-norm on a symmetric interval for the canonical basis
title_short	Polynomial degree reduction in the L2-norm on a symmetric interval for the canonical basis
title_full	Polynomial degree reduction in the L2-norm on a symmetric interval for the canonical basis
title_fullStr	Polynomial degree reduction in the L2-norm on a symmetric interval for the canonical basis
title_full_unstemmed	Polynomial degree reduction in the L2-norm on a symmetric interval for the canonical basis
title_sort	polynomial degree reduction in the l2-norm on a symmetric interval for the canonical basis
publisher	Elsevier
series	Results in Applied Mathematics
issn	2590-0374
publishDate	2021-11-01
description	In this paper, we develop a direct formula for determining the coefficients in the canonical basis of the best polynomial of degree M that approximates a polynomial of degree N>Mon a symmetric interval for the L2-norm. We also formally prove that using the formula is more computationally efficient than using a classical matrix multiplication approach and we provide an example to illustrate that it is more numerically stable than the classical approach.
topic	Polynomial degree reduction Legendre polynomials Optimization Euclidian norm Canonical basis
url	http://www.sciencedirect.com/science/article/pii/S2590037421000352
work_keys_str_mv	AT habibbenabdallah polynomialdegreereductioninthel2normonasymmetricintervalforthecanonicalbasis AT christopherjhenry polynomialdegreereductioninthel2normonasymmetricintervalforthecanonicalbasis AT sheelaramanna polynomialdegreereductioninthel2normonasymmetricintervalforthecanonicalbasis
_version_	1717369870813757440

Polynomial degree reduction in the L2-norm on a symmetric interval for the canonical basis

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