Gaussian extended cubature formulae for polyharmonic functions

Detalhes bibliográficos
Autor(a) principal: Bojanov, Borislav D.
Data de Publicação: 2001
Outros Autores: Dimitrov, Dimitar K. [UNESP]
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.1090/S0025-5718-00-01206-0
http://hdl.handle.net/11449/66486
Resumo: The purpose of this paper is to show certain links between univariate interpolation by algebraic polynomials and the representation of polyharmonic functions. This allows us to construct cubature formulae for multivariate functions having highest order of precision with respect to the class of polyharmonic functions. We obtain a Gauss type cubature formula that uses ℳ values of linear functional (integrals over hyperspheres) and is exact for all 2ℳ-harmonic functions, and consequently, for all algebraic polynomials of n variables of degree 4ℳ - 1.
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spelling Gaussian extended cubature formulae for polyharmonic functionsExtended cubature formulaGaussian extended cubature formulaPolyharmonic functionPolyharmonic order of precisionThe purpose of this paper is to show certain links between univariate interpolation by algebraic polynomials and the representation of polyharmonic functions. This allows us to construct cubature formulae for multivariate functions having highest order of precision with respect to the class of polyharmonic functions. We obtain a Gauss type cubature formula that uses ℳ values of linear functional (integrals over hyperspheres) and is exact for all 2ℳ-harmonic functions, and consequently, for all algebraic polynomials of n variables of degree 4ℳ - 1.Department of Mathematics University of Sofia, James Boucher 5, 1126 SofiaDepto. de Ciencias de Comp. e Estat. IBILCE Univ. Estadual Paulista, 15054-000 Sao Jose do Rio Preto, SPDepto. de Ciencias de Comp. e Estat. IBILCE Univ. Estadual Paulista, 15054-000 Sao Jose do Rio Preto, SPUniversity of SofiaUniversidade Estadual Paulista (Unesp)Bojanov, Borislav D.Dimitrov, Dimitar K. [UNESP]2014-05-27T11:20:15Z2014-05-27T11:20:15Z2001-04-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article671-683http://dx.doi.org/10.1090/S0025-5718-00-01206-0Mathematics of Computation, v. 70, n. 234, p. 671-683, 2001.0025-5718http://hdl.handle.net/11449/6648610.1090/S0025-5718-00-01206-0WOS:0001677384000132-s2.0-0035531380Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengMathematics of Computation1.7501,939info:eu-repo/semantics/openAccess2021-10-23T11:43:22Zoai:repositorio.unesp.br:11449/66486Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462021-10-23T11:43:22Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Gaussian extended cubature formulae for polyharmonic functions
title Gaussian extended cubature formulae for polyharmonic functions
spellingShingle Gaussian extended cubature formulae for polyharmonic functions
Bojanov, Borislav D.
Extended cubature formula
Gaussian extended cubature formula
Polyharmonic function
Polyharmonic order of precision
title_short Gaussian extended cubature formulae for polyharmonic functions
title_full Gaussian extended cubature formulae for polyharmonic functions
title_fullStr Gaussian extended cubature formulae for polyharmonic functions
title_full_unstemmed Gaussian extended cubature formulae for polyharmonic functions
title_sort Gaussian extended cubature formulae for polyharmonic functions
author Bojanov, Borislav D.
author_facet Bojanov, Borislav D.
Dimitrov, Dimitar K. [UNESP]
author_role author
author2 Dimitrov, Dimitar K. [UNESP]
author2_role author
dc.contributor.none.fl_str_mv University of Sofia
Universidade Estadual Paulista (Unesp)
dc.contributor.author.fl_str_mv Bojanov, Borislav D.
Dimitrov, Dimitar K. [UNESP]
dc.subject.por.fl_str_mv Extended cubature formula
Gaussian extended cubature formula
Polyharmonic function
Polyharmonic order of precision
topic Extended cubature formula
Gaussian extended cubature formula
Polyharmonic function
Polyharmonic order of precision
description The purpose of this paper is to show certain links between univariate interpolation by algebraic polynomials and the representation of polyharmonic functions. This allows us to construct cubature formulae for multivariate functions having highest order of precision with respect to the class of polyharmonic functions. We obtain a Gauss type cubature formula that uses ℳ values of linear functional (integrals over hyperspheres) and is exact for all 2ℳ-harmonic functions, and consequently, for all algebraic polynomials of n variables of degree 4ℳ - 1.
publishDate 2001
dc.date.none.fl_str_mv 2001-04-01
2014-05-27T11:20:15Z
2014-05-27T11:20:15Z
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/10.1090/S0025-5718-00-01206-0
Mathematics of Computation, v. 70, n. 234, p. 671-683, 2001.
0025-5718
http://hdl.handle.net/11449/66486
10.1090/S0025-5718-00-01206-0
WOS:000167738400013
2-s2.0-0035531380
url http://dx.doi.org/10.1090/S0025-5718-00-01206-0
http://hdl.handle.net/11449/66486
identifier_str_mv Mathematics of Computation, v. 70, n. 234, p. 671-683, 2001.
0025-5718
10.1090/S0025-5718-00-01206-0
WOS:000167738400013
2-s2.0-0035531380
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Mathematics of Computation
1.750
1,939
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 671-683
dc.source.none.fl_str_mv Scopus
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
_version_ 1799965474522398720

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