This article is cited in 2 papers

Mathematics

On a conjecture in bivariate interpolation

S. Z. Toroyan

Yerevan State University

Abstract: 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: polynomial interpolation, poised, independent nodes, algebraic curves.

MSC: Primary 41A05; Secondary 14H50

Received: 18.01.2016
Accepted: 25.02.2016

Language: English