Observations on interpolation by total degree polynomials in two variables

Carnicer, Jesús (Universidad de Zaragoza) ; Sauer, Tomás

Resumen: In contrast to the univariate case, interpolation with polynomials of a given maximal total degree is not always possible even if the number of interpolation points and the space dimension coincide. Due to that, numerous constructions for interpolation sets have been devised, the most popular ones being based on intersections of lines. In this paper, we study algebraic properties of some such interpolation configurations, namely the approaches by Radon–Berzolari and Chung–Yao. By means of proper H-bases for the vanishing ideal of the configuration, we derive properties of the matrix of first syzygies of this ideal that allow us to draw conclusions on the geometry of the point configuration.

Idioma: Inglés

DOI: 10.1007/s00365-017-9380-8

Año: 2017

Publicado en: CONSTRUCTIVE APPROXIMATION 47, 3 (2017), 373-389 [16 p.]
ISSN: 0176-4276

Factor impacto JCR: 0.827 (2017)

Categ. JCR: MATHEMATICS rank: 116 / 309 = 0.375 (2017) - Q2 - T2

Factor impacto SCIMAGO: 0.738 - Analysis (Q2) - Mathematics (miscellaneous) (Q2) - Computational Mathematics (Q2)

Financiación: info:eu-repo/grantAgreement/ES/MINECO-FEDER/MTM2015-65433-P

Tipo y forma: Artículo (PostPrint)

Área (Departamento): Área Matemática Aplicada (Dpto. Matemática Aplicada)