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AN EFFICIENT ALGORITHM FOR THE CLASSICAL LEAST SQUARES APPROXIMATION

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dc.contributor.authorDimitrov, Dimitar K. [UNESP]
dc.contributor.authorPeixoto, Lourenco L.
dc.contributor.institutionUniversidade Estadual Paulista (Unesp)
dc.contributor.institutionInst Fed Minas Gerais
dc.date.accessioned2021-06-25T12:29:53Z
dc.date.available2021-06-25T12:29:53Z
dc.date.issued2020-01-01
dc.description.abstractWe 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.en
dc.description.affiliationUniv Estadual Paulista, Dept Matemat, IBILCE, BR-15054000 Sao Jose Do Rio Preto, SP, Brazil
dc.description.affiliationInst Fed Minas Gerais, Dept Matemat, BR-36415000 Congonhas, MG, Brazil
dc.description.affiliationUnespUniv Estadual Paulista, Dept Matemat, IBILCE, BR-15054000 Sao Jose Do Rio Preto, SP, Brazil
dc.description.sponsorshipFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
dc.description.sponsorshipConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
dc.description.sponsorshipCoordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
dc.description.sponsorshipIdFAPESP: 2016/09906-0
dc.description.sponsorshipIdCNPq: 306136/2017-1
dc.description.sponsorshipIdCAPES: 23038010617201/334
dc.format.extentA3233-A3249
dc.identifierhttp://dx.doi.org/10.1137/19M1259936
dc.identifier.citationSiam Journal On Scientific Computing. Philadelphia: Siam Publications, v. 42, n. 5, p. A3233-A3249, 2020.
dc.identifier.dimensionspub.1131901413
dc.identifier.doi10.1137/19M1259936
dc.identifier.issn1064-8275
dc.identifier.issn1095-7197
dc.identifier.orcid0000-0001-8448-242X
dc.identifier.orcid0000-0002-3078-2336
dc.identifier.urihttp://hdl.handle.net/11449/209807
dc.identifier.wosWOS:000600650100011
dc.language.isoeng
dc.publisherSiam Publications
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)
dc.relation.ispartofSiam Journal On Scientific Computing
dc.rights.accessRightsAcesso abertopt
dc.rights.sourceRightsoa_all
dc.rights.sourceRightsgreen
dc.sourceWeb of Science
dc.sourceDimensions
dc.subjectleast squares approximation
dc.subjectGaussian quadrature
dc.subjectorthogonal Gram polynomials
dc.subjectWDDK method
dc.subjectNewton-Raphson method
dc.subjectGolub-Welsch algorithm
dc.titleAN EFFICIENT ALGORITHM FOR THE CLASSICAL LEAST SQUARES APPROXIMATIONen
dc.typeArtigopt
dcterms.rightsHolderSiam Publications
dspace.entity.typePublication
relation.isOrgUnitOfPublication43c38943-bd6f-4fb6-a9a5-8482a1f632c0
relation.isOrgUnitOfPublication.latestForDiscovery43c38943-bd6f-4fb6-a9a5-8482a1f632c0
unesp.author.orcid0000-0002-3078-2336[1]
unesp.campusUniversidade Estadual Paulista (UNESP), Instituto de Biociências, Letras e Ciências Exatas, São José do Rio Pretopt
unesp.departmentMatemática - IBILCEpt

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São José do Rio Preto - IBILCE - Instituto de Biociências, Letras e Ciências Exatas