Integration of polyharmonic functions

Detalhes bibliográficos
Autor(a) principal: Dimitrov, D. K.
Data de Publicação: 1996
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.1090/S0025-5718-96-00747-8
http://hdl.handle.net/11449/37891
Resumo: The results in this paper are motivated by two analogies. First, m-harmonic functions in R(n) are extensions of the univariate algebraic polynomials of odd degree 2m-1. Second, Gauss' and Pizzetti's mean value formulae are natural multivariate analogues of the rectangular and Taylor's quadrature formulae, respectively. This point of view suggests that some theorems concerning quadrature rules could be generalized to results about integration of polyharmonic functions. This is done for the Tchakaloff-Obrechkoff quadrature formula and for the Gaussian quadrature with two nodes.
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spelling Integration of polyharmonic functionspolyharmonic functionextended cubature formulapolyharmonic order of precisionpolyharmonic monosplineThe results in this paper are motivated by two analogies. First, m-harmonic functions in R(n) are extensions of the univariate algebraic polynomials of odd degree 2m-1. Second, Gauss' and Pizzetti's mean value formulae are natural multivariate analogues of the rectangular and Taylor's quadrature formulae, respectively. This point of view suggests that some theorems concerning quadrature rules could be generalized to results about integration of polyharmonic functions. This is done for the Tchakaloff-Obrechkoff quadrature formula and for the Gaussian quadrature with two nodes.UNIV ESTADUAL PAULISTA,DEPT CIENCIAS COMP & ESTATIST,IBILCE,BR-15054000 S JOSE RIO PR,SP,BRAZILUNIV ESTADUAL PAULISTA,DEPT CIENCIAS COMP & ESTATIST,IBILCE,BR-15054000 S JOSE RIO PR,SP,BRAZILAmer Mathematical SocUniversidade Estadual Paulista (Unesp)Dimitrov, D. K.2014-05-20T15:27:59Z2014-05-20T15:27:59Z1996-07-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article1269-1281http://dx.doi.org/10.1090/S0025-5718-96-00747-8Mathematics of Computation. Providence: Amer Mathematical Soc, v. 65, n. 215, p. 1269-1281, 1996.0025-5718http://hdl.handle.net/11449/3789110.1090/S0025-5718-96-00747-8WOS:A1996UR114000211681267716971253Web of Sciencereponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengMathematics of Computation1.7501,939info:eu-repo/semantics/openAccess2021-10-23T11:33:37Zoai:repositorio.unesp.br:11449/37891Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462021-10-23T11:33:37Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Integration of polyharmonic functions
title Integration of polyharmonic functions
spellingShingle Integration of polyharmonic functions
Dimitrov, D. K.
polyharmonic function
extended cubature formula
polyharmonic order of precision
polyharmonic monospline
title_short Integration of polyharmonic functions
title_full Integration of polyharmonic functions
title_fullStr Integration of polyharmonic functions
title_full_unstemmed Integration of polyharmonic functions
title_sort Integration of polyharmonic functions
author Dimitrov, D. K.
author_facet Dimitrov, D. K.
author_role author
dc.contributor.none.fl_str_mv Universidade Estadual Paulista (Unesp)
dc.contributor.author.fl_str_mv Dimitrov, D. K.
dc.subject.por.fl_str_mv polyharmonic function
extended cubature formula
polyharmonic order of precision
polyharmonic monospline
topic polyharmonic function
extended cubature formula
polyharmonic order of precision
polyharmonic monospline
description The results in this paper are motivated by two analogies. First, m-harmonic functions in R(n) are extensions of the univariate algebraic polynomials of odd degree 2m-1. Second, Gauss' and Pizzetti's mean value formulae are natural multivariate analogues of the rectangular and Taylor's quadrature formulae, respectively. This point of view suggests that some theorems concerning quadrature rules could be generalized to results about integration of polyharmonic functions. This is done for the Tchakaloff-Obrechkoff quadrature formula and for the Gaussian quadrature with two nodes.
publishDate 1996
dc.date.none.fl_str_mv 1996-07-01
2014-05-20T15:27:59Z
2014-05-20T15:27:59Z
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/S0025-5718-96-00747-8
Mathematics of Computation. Providence: Amer Mathematical Soc, v. 65, n. 215, p. 1269-1281, 1996.
0025-5718
http://hdl.handle.net/11449/37891
10.1090/S0025-5718-96-00747-8
WOS:A1996UR11400021
1681267716971253
url http://dx.doi.org/10.1090/S0025-5718-96-00747-8
http://hdl.handle.net/11449/37891
identifier_str_mv Mathematics of Computation. Providence: Amer Mathematical Soc, v. 65, n. 215, p. 1269-1281, 1996.
0025-5718
10.1090/S0025-5718-96-00747-8
WOS:A1996UR11400021
1681267716971253
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 1269-1281
dc.publisher.none.fl_str_mv Amer Mathematical Soc
publisher.none.fl_str_mv Amer Mathematical Soc
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
_version_ 1799964738125299712

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