AN EFFICIENT ALGORITHM FOR THE CLASSICAL LEAST SQUARES APPROXIMATION
| dc.contributor.author | Dimitrov, Dimitar K. [UNESP] | |
| dc.contributor.author | Peixoto, Lourenco L. | |
| dc.contributor.institution | Universidade Estadual Paulista (Unesp) | |
| dc.contributor.institution | Inst Fed Minas Gerais | |
| dc.date.accessioned | 2021-06-25T12:29:53Z | |
| dc.date.available | 2021-06-25T12:29:53Z | |
| dc.date.issued | 2020-01-01 | |
| dc.description.abstract | 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. | en |
| dc.description.affiliation | Univ Estadual Paulista, Dept Matemat, IBILCE, BR-15054000 Sao Jose Do Rio Preto, SP, Brazil | |
| dc.description.affiliation | Inst Fed Minas Gerais, Dept Matemat, BR-36415000 Congonhas, MG, Brazil | |
| dc.description.affiliationUnesp | Univ Estadual Paulista, Dept Matemat, IBILCE, BR-15054000 Sao Jose Do Rio Preto, SP, Brazil | |
| dc.description.sponsorship | Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) | |
| dc.description.sponsorship | Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) | |
| dc.description.sponsorship | Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) | |
| dc.description.sponsorshipId | FAPESP: 2016/09906-0 | |
| dc.description.sponsorshipId | CNPq: 306136/2017-1 | |
| dc.description.sponsorshipId | CAPES: 23038010617201/334 | |
| dc.format.extent | A3233-A3249 | |
| dc.identifier | http://dx.doi.org/10.1137/19M1259936 | |
| dc.identifier.citation | Siam Journal On Scientific Computing. Philadelphia: Siam Publications, v. 42, n. 5, p. A3233-A3249, 2020. | |
| dc.identifier.doi | 10.1137/19M1259936 | |
| dc.identifier.issn | 1064-8275 | |
| dc.identifier.uri | http://hdl.handle.net/11449/209807 | |
| dc.identifier.wos | WOS:000600650100011 | |
| dc.language.iso | eng | |
| dc.publisher | Siam Publications | |
| dc.relation.ispartof | Siam Journal On Scientific Computing | |
| dc.source | Web of Science | |
| dc.subject | least squares approximation | |
| dc.subject | Gaussian quadrature | |
| dc.subject | orthogonal Gram polynomials | |
| dc.subject | WDDK method | |
| dc.subject | Newton-Raphson method | |
| dc.subject | Golub-Welsch algorithm | |
| dc.title | AN EFFICIENT ALGORITHM FOR THE CLASSICAL LEAST SQUARES APPROXIMATION | en |
| dc.type | Artigo | |
| dcterms.rightsHolder | Siam Publications | |
| unesp.author.orcid | 0000-0002-3078-2336[1] |