Expected term bases for generic multivariate Hermite interpolation Article

First Online: 06 July 2007 Received: 18 October 2004 Revised: 09 May 2007 DOI :
10.1007/s00200-007-0049-6

Cite this article as: Dumnicki, M. AAECC (2007) 18: 467. doi:10.1007/s00200-007-0049-6
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

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Authors and Affiliations 1. Institute of Mathematics Jagiellonian University Kraków Poland