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Abstract:

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.

Registro:

Documento: Artículo
Título:Subresultants, Sylvester sums and the rational interpolation problem
Autor:D'Andrea, C.; Krick, T.; Szanto, A.
Filiación:Universitat de Barcelona, Departament d'Àlgebra i Geometria, Gran Via 585, Barcelona, 08007, Spain
Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires and IMAS, CONICET, Argentina
Department of Mathematics, North Carolina State University, Raleigh, NC 27695, United States
Palabras clave:Cauchy interpolation; Osculatory interpolation; Rational Hermite interpolation; Rational interpolation; Subresultants; Sylvester sums
Año:2015
Volumen:68
Número:P1
Página de inicio:72
Página de fin:83
DOI: http://dx.doi.org/10.1016/j.jsc.2014.08.008
Título revista:Journal of Symbolic Computation
Título revista abreviado:J. Symb. Comput.
ISSN:07477171
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_07477171_v68_nP1_p72_DAndrea

Referencias:

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Citas:

---------- APA ----------
D'Andrea, C., Krick, T. & Szanto, A. (2015) . Subresultants, Sylvester sums and the rational interpolation problem. Journal of Symbolic Computation, 68(P1), 72-83.
http://dx.doi.org/10.1016/j.jsc.2014.08.008
---------- CHICAGO ----------
D'Andrea, C., Krick, T., Szanto, A. "Subresultants, Sylvester sums and the rational interpolation problem" . Journal of Symbolic Computation 68, no. P1 (2015) : 72-83.
http://dx.doi.org/10.1016/j.jsc.2014.08.008
---------- MLA ----------
D'Andrea, C., Krick, T., Szanto, A. "Subresultants, Sylvester sums and the rational interpolation problem" . Journal of Symbolic Computation, vol. 68, no. P1, 2015, pp. 72-83.
http://dx.doi.org/10.1016/j.jsc.2014.08.008
---------- VANCOUVER ----------
D'Andrea, C., Krick, T., Szanto, A. Subresultants, Sylvester sums and the rational interpolation problem. J. Symb. Comput. 2015;68(P1):72-83.
http://dx.doi.org/10.1016/j.jsc.2014.08.008