This article is cited in 5 papers

Mathematics

On the minimal number of nodes uniquely determining algebraic curves

H. A. Hakopian, S. Z. Toroyan

Yerevan State University

Abstract: It is well-known that the number of $n$-independent nodes determining uniquely the curve of degree $n$ passing through them equals to $N-1$, where $N=\dfrac{1}{2}(n+1)(n+2)$. It was proved in [1], that the minimal number of $n$-independent nodes determining uniquely the curve of degree $n-1$ equals to $N-4$. The paper also posed a conjecture concerning the analogous problem for general degree $k\leq n$. In the present paper the conjecture is proved, establishing that the minimal number of $n$-independent nodes determining uniquely the curve of degree $k\leq n$ equals to $\dfrac{(k-1)(2n+4-k)}{2}+2$.

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

MSC: Primary 41A05; Secondary 14H50

Received: 07.05.2015
Revised: 30.06.2015

Language: English