Article

Applicable Algebra in Engineering, Communication and Computing

, Volume 18, Issue 5, pp 467-482

First online:

Expected term bases for generic multivariate Hermite interpolation

  • Marcin DumnickiAffiliated withInstitute of Mathematics, Jagiellonian University Email author 

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Abstract

The main goal of the paper is to find an effective estimation for the minimal number of points in \({\mathbb{K}}^{2}\) in general position for which the basis for Hermite interpolation consists of the first ℓ terms (with respect to total degree ordering). As a result we prove that the space of plane curves of degree at most d having singularities of multiplicity ≤ m in general position has the expected dimension if the number of low order singularities (of multiplicity k ≤ 12) is greater then some r(m, k). Additionally, the upper bounds for r(m, k) are given.

Keywords

Multivariate interpolation Algebraic curves