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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Autores principales: D'Andrea, C., Krick, T., Szanto, A.
Formato: JOUR
Materias:
Cauchy interpolation
Osculatory interpolation
Rational Hermite interpolation
Rational interpolation
Subresultants
Sylvester sums
Acceso en línea: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 todo:paper_07477171_v68_nP1_p72_DAndrea
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spelling todo:paper_07477171_v68_nP1_p72_DAndrea2023-10-03T15:38:59Z Subresultants, Sylvester sums and the rational interpolation problem D'Andrea, C. Krick, T. Szanto, A. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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, C.
Krick, T.
Szanto, A.
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.
format JOUR
author D'Andrea, C.
Krick, T.
Szanto, A.
author_facet D'Andrea, C.
Krick, T.
Szanto, A.
author_sort D'Andrea, C.
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
url http://hdl.handle.net/20.500.12110/paper_07477171_v68_nP1_p72_DAndrea
work_keys_str_mv AT dandreac subresultantssylvestersumsandtherationalinterpolationproblem
AT krickt subresultantssylvestersumsandtherationalinterpolationproblem
AT szantoa subresultantssylvestersumsandtherationalinterpolationproblem
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