Characterization of ɳ-independent sets with no more than 3ɳ points

• H. Hakopian ^[1] ; A. Malinyan ^[2]
  1. [1] Yerevan State University

     Yerevan State University

     Armenia

     
  2. [2] Armenian-Russian (Slavonic) University
• Localización: Jaen journal on approximation, ISSN 1889-3066, ISSN-e 1989-7251, Vol. 4, Nº. 2, 2012, págs. 121-136
• Idioma: inglés
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• Resumen

  • Let Πn denote the space of all bivariate polynomials of total degree not exceeding n. We study the n-independence of point sets. These sets X are characterized by the fact that the dimension of the space PX = {p ∈ Πn : p(x) = 0, ∀x ∈ X } equals dim Πn − #X . Besides, polynomial interpolation of degree n is solvable only with these sets. Moreover, the n-independent sets are exactly the subsets of Πn-poised sets. In this paper we characterize all n-independent sets with no more than 3n points.