AN EFFICIENT ALGORITHM FOR THE CLASSICAL LEAST SQUARES APPROXIMATION

Bibliographic Details
Main Author: Dimitrov, Dimitar K. [UNESP]
Publication Date: 2020
Other Authors: Peixoto, Lourenco L.
Format: Article
Language: eng
Source: Repositório Institucional da UNESP
Download full: http://dx.doi.org/10.1137/19M1259936
http://hdl.handle.net/11449/209807
Summary: We explore the computational issues concerning a new algorithm for the classical least-squares approximation of N samples by an algebraic polynomial of degree at most n when the number N of the samples is very large. The algorithm is based on a recent idea about accurate numerical approximations of sums with large numbers of terms. For a fixed n, the complexity of our algorithm in double precision accuracy is O(1). It is faster and more precise than the standard algorithm in MATLAB.
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spelling AN EFFICIENT ALGORITHM FOR THE CLASSICAL LEAST SQUARES APPROXIMATIONleast squares approximationGaussian quadratureorthogonal Gram polynomialsWDDK methodNewton-Raphson methodGolub-Welsch algorithmWe explore the computational issues concerning a new algorithm for the classical least-squares approximation of N samples by an algebraic polynomial of degree at most n when the number N of the samples is very large. The algorithm is based on a recent idea about accurate numerical approximations of sums with large numbers of terms. For a fixed n, the complexity of our algorithm in double precision accuracy is O(1). It is faster and more precise than the standard algorithm in MATLAB.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Univ Estadual Paulista, Dept Matemat, IBILCE, BR-15054000 Sao Jose Do Rio Preto, SP, BrazilInst Fed Minas Gerais, Dept Matemat, BR-36415000 Congonhas, MG, BrazilUniv Estadual Paulista, Dept Matemat, IBILCE, BR-15054000 Sao Jose Do Rio Preto, SP, BrazilFAPESP: 2016/09906-0CNPq: 306136/2017-1CAPES: 23038010617201/334Siam PublicationsUniversidade Estadual Paulista (Unesp)Inst Fed Minas GeraisDimitrov, Dimitar K. [UNESP]Peixoto, Lourenco L.2021-06-25T12:29:53Z2021-06-25T12:29:53Z2020-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleA3233-A3249http://dx.doi.org/10.1137/19M1259936Siam Journal On Scientific Computing. Philadelphia: Siam Publications, v. 42, n. 5, p. A3233-A3249, 2020.1064-8275http://hdl.handle.net/11449/20980710.1137/19M1259936WOS:000600650100011Web of Sciencereponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengSiam Journal On Scientific Computinginfo:eu-repo/semantics/openAccess2024-11-01T14:27:23Zoai:repositorio.unesp.br:11449/209807Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestrepositoriounesp@unesp.bropendoar:29462024-11-01T14:27:23Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv AN EFFICIENT ALGORITHM FOR THE CLASSICAL LEAST SQUARES APPROXIMATION
title AN EFFICIENT ALGORITHM FOR THE CLASSICAL LEAST SQUARES APPROXIMATION
spellingShingle AN EFFICIENT ALGORITHM FOR THE CLASSICAL LEAST SQUARES APPROXIMATION
Dimitrov, Dimitar K. [UNESP]
least squares approximation
Gaussian quadrature
orthogonal Gram polynomials
WDDK method
Newton-Raphson method
Golub-Welsch algorithm
title_short AN EFFICIENT ALGORITHM FOR THE CLASSICAL LEAST SQUARES APPROXIMATION
title_full AN EFFICIENT ALGORITHM FOR THE CLASSICAL LEAST SQUARES APPROXIMATION
title_fullStr AN EFFICIENT ALGORITHM FOR THE CLASSICAL LEAST SQUARES APPROXIMATION
title_full_unstemmed AN EFFICIENT ALGORITHM FOR THE CLASSICAL LEAST SQUARES APPROXIMATION
title_sort AN EFFICIENT ALGORITHM FOR THE CLASSICAL LEAST SQUARES APPROXIMATION
author Dimitrov, Dimitar K. [UNESP]
author_facet Dimitrov, Dimitar K. [UNESP]
Peixoto, Lourenco L.
author_role author
author2 Peixoto, Lourenco L.
author2_role author
dc.contributor.none.fl_str_mv Universidade Estadual Paulista (Unesp)
Inst Fed Minas Gerais
dc.contributor.author.fl_str_mv Dimitrov, Dimitar K. [UNESP]
Peixoto, Lourenco L.
dc.subject.por.fl_str_mv least squares approximation
Gaussian quadrature
orthogonal Gram polynomials
WDDK method
Newton-Raphson method
Golub-Welsch algorithm
topic least squares approximation
Gaussian quadrature
orthogonal Gram polynomials
WDDK method
Newton-Raphson method
Golub-Welsch algorithm
description We explore the computational issues concerning a new algorithm for the classical least-squares approximation of N samples by an algebraic polynomial of degree at most n when the number N of the samples is very large. The algorithm is based on a recent idea about accurate numerical approximations of sums with large numbers of terms. For a fixed n, the complexity of our algorithm in double precision accuracy is O(1). It is faster and more precise than the standard algorithm in MATLAB.
publishDate 2020
dc.date.none.fl_str_mv 2020-01-01
2021-06-25T12:29:53Z
2021-06-25T12:29:53Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://dx.doi.org/10.1137/19M1259936
Siam Journal On Scientific Computing. Philadelphia: Siam Publications, v. 42, n. 5, p. A3233-A3249, 2020.
1064-8275
http://hdl.handle.net/11449/209807
10.1137/19M1259936
WOS:000600650100011
url http://dx.doi.org/10.1137/19M1259936
http://hdl.handle.net/11449/209807
identifier_str_mv Siam Journal On Scientific Computing. Philadelphia: Siam Publications, v. 42, n. 5, p. A3233-A3249, 2020.
1064-8275
10.1137/19M1259936
WOS:000600650100011
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Siam Journal On Scientific Computing
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv A3233-A3249
dc.publisher.none.fl_str_mv Siam Publications
publisher.none.fl_str_mv Siam Publications
dc.source.none.fl_str_mv Web of Science
reponame:Repositório Institucional da UNESP
instname:Universidade Estadual Paulista (UNESP)
instacron:UNESP
instname_str Universidade Estadual Paulista (UNESP)
instacron_str UNESP
institution UNESP
reponame_str Repositório Institucional da UNESP
collection Repositório Institucional da UNESP
repository.name.fl_str_mv Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)
repository.mail.fl_str_mv repositoriounesp@unesp.br
_version_ 1834484662362177536

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