A six-dimensional counterexample for the GMᶑ conjecture
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Armen Apozyan [1]
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[1] Institute of Mathematics of National Academy of Sciences of Armenia
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- Localización: Jaen journal on approximation, ISSN 1889-3066, ISSN-e 1989-7251, Vol. 3, Nº. 2, 2011, págs. 161-172
- Idioma: inglés
- Texto completo no disponible (Saber más ...)
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Resumen
The conjecture GMd by C. de Boor was based on a conjecture by M. Gasca and J.I. Maeztu about interpolation in the plane. This conjecture was formulated by M. Gasca and J. I. Maeztu to argue that the construction of Newton formula based on the system of interpolation nodes of Berzolari and Radon was more general and covered all examples of sets satisfying the geometric characterization described by Chung and Yao. Some examples and facts observed in planar examples seemed to suggest that the system of interpolation nodes of Berzolari and Radon could describe much more examples than the Chung and Yao construction and even that each GC set in any dimension could be described as a set of interpolation nodes obtained by a multidimensional generalization of Berzolari-Radon construction.
In this paper we provide a counterexample which shows that, at least in R 6,there are GC sets that cannot be described as the set of interpolation nodes of Berzolari-Radon interpolation system.
