Subresultants, sylvester sums and the rational interpolation problem

Autores
D'Andrea, Carlos; Krick, Teresa Elena Genoveva; Szanto, Agnes
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We present a solution for the classical univariate rational interpolation problem by means of (univariate) subresultants. In the case of Cauchy interpolation (interpolation without multiplicities), we give explicit formulas for the solution in terms of symmetric functions of the input data, generalizing the well-known formulas for Lagrange interpolation. In the case of the osculatory rational interpolation (interpolation with multiplicities), we give determinantal expressions in terms of the input data, making explicit some matrix formulations that can independently be derived from previous results by Beckermann and Labahn.
Fil: D'Andrea, Carlos. Universidad de Barcelona; España
Fil: Krick, Teresa Elena Genoveva. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Szanto, Agnes. North Carolina State University; Estados Unidos
Materia
Rational Interpolation
Subresultants
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/18916
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/18916
network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling Subresultants, sylvester sums and the rational interpolation problemD'Andrea, CarlosKrick, Teresa Elena GenovevaSzanto, AgnesRational InterpolationSubresultantshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We present a solution for the classical univariate rational interpolation problem by means of (univariate) subresultants. In the case of Cauchy interpolation (interpolation without multiplicities), we give explicit formulas for the solution in terms of symmetric functions of the input data, generalizing the well-known formulas for Lagrange interpolation. In the case of the osculatory rational interpolation (interpolation with multiplicities), we give determinantal expressions in terms of the input data, making explicit some matrix formulations that can independently be derived from previous results by Beckermann and Labahn.Fil: D'Andrea, Carlos. Universidad de Barcelona; EspañaFil: Krick, Teresa Elena Genoveva. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Szanto, Agnes. North Carolina State University; Estados UnidosElsevier2015-06info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/18916D'Andrea, Carlos; Krick, Teresa Elena Genoveva; Szanto, Agnes; Subresultants, sylvester sums and the rational interpolation problem; Elsevier; Journal Of Symbolic Computation; 68; Part 1; 6-2015; 72-830747-7171CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.jsc.2014.08.008info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0747717114000583info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1211.6895info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:46:36Zoai:ri.conicet.gov.ar:11336/18916instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-03 09:46:36.63CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Subresultants, sylvester sums and the rational interpolation problem
title Subresultants, sylvester sums and the rational interpolation problem
spellingShingle Subresultants, sylvester sums and the rational interpolation problem
D'Andrea, Carlos
Rational Interpolation
Subresultants
title_short Subresultants, sylvester sums and the rational interpolation problem
title_full Subresultants, sylvester sums and the rational interpolation problem
title_fullStr Subresultants, sylvester sums and the rational interpolation problem
title_full_unstemmed Subresultants, sylvester sums and the rational interpolation problem
title_sort Subresultants, sylvester sums and the rational interpolation problem
dc.creator.none.fl_str_mv D'Andrea, Carlos
Krick, Teresa Elena Genoveva
Szanto, Agnes
author D'Andrea, Carlos
author_facet D'Andrea, Carlos
Krick, Teresa Elena Genoveva
Szanto, Agnes
author_role author
author2 Krick, Teresa Elena Genoveva
Szanto, Agnes
author2_role author
author
dc.subject.none.fl_str_mv Rational Interpolation
Subresultants
topic Rational Interpolation
Subresultants
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We present a solution for the classical univariate rational interpolation problem by means of (univariate) subresultants. In the case of Cauchy interpolation (interpolation without multiplicities), we give explicit formulas for the solution in terms of symmetric functions of the input data, generalizing the well-known formulas for Lagrange interpolation. In the case of the osculatory rational interpolation (interpolation with multiplicities), we give determinantal expressions in terms of the input data, making explicit some matrix formulations that can independently be derived from previous results by Beckermann and Labahn.
Fil: D'Andrea, Carlos. Universidad de Barcelona; España
Fil: Krick, Teresa Elena Genoveva. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Szanto, Agnes. North Carolina State University; Estados Unidos
description We present a solution for the classical univariate rational interpolation problem by means of (univariate) subresultants. In the case of Cauchy interpolation (interpolation without multiplicities), we give explicit formulas for the solution in terms of symmetric functions of the input data, generalizing the well-known formulas for Lagrange interpolation. In the case of the osculatory rational interpolation (interpolation with multiplicities), we give determinantal expressions in terms of the input data, making explicit some matrix formulations that can independently be derived from previous results by Beckermann and Labahn.
publishDate 2015
dc.date.none.fl_str_mv 2015-06
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/18916
D'Andrea, Carlos; Krick, Teresa Elena Genoveva; Szanto, Agnes; Subresultants, sylvester sums and the rational interpolation problem; Elsevier; Journal Of Symbolic Computation; 68; Part 1; 6-2015; 72-83
0747-7171
CONICET Digital
CONICET
url http://hdl.handle.net/11336/18916
identifier_str_mv D'Andrea, Carlos; Krick, Teresa Elena Genoveva; Szanto, Agnes; Subresultants, sylvester sums and the rational interpolation problem; Elsevier; Journal Of Symbolic Computation; 68; Part 1; 6-2015; 72-83
0747-7171
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jsc.2014.08.008
info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0747717114000583
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1211.6895
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
_version_ 1842268805659623424
score 13.13397

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