Abstract
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.
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Acknowledgements
We a very grateful to Hal Schenck for the discussions on a draft of his paper that helped us to write this paper and to Carl de Boor for a lot of valuable remarks and comments on the first draft that greatly improved the presentation.
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Communicated by Carl de Boor.
J. Carnicer was partially supported by MTM2015-65433-P (MINECO/FEDER) Spanish Research Grant, by Gobierno de Aragón and European Social Fund.
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Carnicer, J., Sauer, T. Observations on Interpolation by Total Degree Polynomials in Two Variables. Constr Approx 47, 373–389 (2018). https://doi.org/10.1007/s00365-017-9380-8
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DOI: https://doi.org/10.1007/s00365-017-9380-8