Subresultants, Sylvester sums and the rational interpolation problem

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, generali...

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Detalles Bibliográficos
Autores principales:	D'Andrea, Carlos Antonio, Krick, Teresa Elena Genoveva
Publicado:	2015
Materias:	Cauchy interpolation Osculatory interpolation Rational Hermite interpolation Rational interpolation Subresultants Sylvester sums
Acceso en línea:	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_07477171_v68_nP1_p72_DAndrea http://hdl.handle.net/20.500.12110/paper_07477171_v68_nP1_p72_DAndrea
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	paper:paper_07477171_v68_nP1_p72_DAndrea
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spelling	paper:paper_07477171_v68_nP1_p72_DAndrea2023-06-08T15:45:12Z Subresultants, Sylvester sums and the rational interpolation problem D'Andrea, Carlos Antonio Krick, Teresa Elena Genoveva Cauchy interpolation Osculatory interpolation Rational Hermite interpolation Rational interpolation Subresultants Sylvester sums 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. © 2014 Elsevier Ltd. Fil:D'Andrea, C. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Krick, T. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2015 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_07477171_v68_nP1_p72_DAndrea http://hdl.handle.net/20.500.12110/paper_07477171_v68_nP1_p72_DAndrea
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	Cauchy interpolation Osculatory interpolation Rational Hermite interpolation Rational interpolation Subresultants Sylvester sums
spellingShingle	Cauchy interpolation Osculatory interpolation Rational Hermite interpolation Rational interpolation Subresultants Sylvester sums D'Andrea, Carlos Antonio Krick, Teresa Elena Genoveva Subresultants, Sylvester sums and the rational interpolation problem
topic_facet	Cauchy interpolation Osculatory interpolation Rational Hermite interpolation Rational interpolation Subresultants Sylvester sums
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. © 2014 Elsevier Ltd.
author	D'Andrea, Carlos Antonio Krick, Teresa Elena Genoveva
author_facet	D'Andrea, Carlos Antonio Krick, Teresa Elena Genoveva
author_sort	D'Andrea, Carlos Antonio
title	Subresultants, Sylvester sums and the rational interpolation problem
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
publishDate	2015
url	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_07477171_v68_nP1_p72_DAndrea http://hdl.handle.net/20.500.12110/paper_07477171_v68_nP1_p72_DAndrea
work_keys_str_mv	AT dandreacarlosantonio subresultantssylvestersumsandtherationalinterpolationproblem AT krickteresaelenagenoveva subresultantssylvestersumsandtherationalinterpolationproblem
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Subresultants, Sylvester sums and the rational interpolation problem

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