Gaussian extended cubature formulae for polyharmonic functions
Autor(a) principal: | |
---|---|
Data de Publicação: | 2001 |
Outros Autores: | |
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. |
id |
UNSP_5b5960ba0afb26077c4038e21dc181da |
---|---|
oai_identifier_str |
oai:repositorio.unesp.br:11449/66486 |
network_acronym_str |
UNSP |
network_name_str |
Repositório Institucional da UNESP |
repository_id_str |
2946 |
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:29462024-08-05T21:49:26.310132Repositório 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_ |
1808129362361319424 |