Geodesic
On a conjecture in bivariate interpolation
Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 1 (2016), pp. 30-34

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Denote the space of all bivariate polynomials of total degree $\leq n$ by $\Pi_n$. We are interested in $n$-poised sets of nodes with the property that the fundamental polynomial of each node is a product of linear factors. In 1981 M. Gasca and J.I.Maeztu conjectured that every such set contains necessarily $n+1$ collinear nodes. Up to now this had been confirmed for degrees $n\leq5$. Here we bring a simple and short proof of the conjecture for $n=4$.
Keywords: poised, independent nodes, algebraic curves.
Mots-clés : polynomial interpolation 
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S. Z. Toroyan. On a conjecture in bivariate interpolation. Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 1 (2016), pp. 30-34. http://geodesic.mathdoc.fr/item/UZERU_2016_1_a4/