ON THE MINIMAL NUMBER OF NODES UNIQUELY DETERMINING ALGEBRAIC CURVES

Authors

  • H.A. Hakopian Chair of Numerical Analysis and Mathematical Modeling, YSU, Armenia
  • S.Z. Toroyan Chair of Numerical Analysis and Mathematical Modeling, YSU, Armenia

DOI:

https://doi.org/10.46991/PYSU:A/2015.49.3.017

Keywords:

polynomial interpolation, poised, independent nodes, algebraic curves

Abstract

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

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Published

2015-12-15

How to Cite

Hakopian, H., & Toroyan, S. (2015). ON THE MINIMAL NUMBER OF NODES UNIQUELY DETERMINING ALGEBRAIC CURVES. Proceedings of the YSU A: Physical and Mathematical Sciences, 49(3 (238), 17–22. https://doi.org/10.46991/PYSU:A/2015.49.3.017

Issue

Section

Mathematics