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Expected term bases for generic multivariate Hermite interpolation

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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.

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  1. Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059, Kraków, Poland

    Marcin Dumnicki

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  1. Marcin Dumnicki
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Correspondence to Marcin Dumnicki.

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Dumnicki, M. Expected term bases for generic multivariate Hermite interpolation. AAECC 18, 467–482 (2007). https://doi.org/10.1007/s00200-007-0049-6

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  • DOI: https://doi.org/10.1007/s00200-007-0049-6

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