Applicable Algebra in Engineering, Communication and Computing

, Volume 18, Issue 5, pp 467–482

Expected term bases for generic multivariate Hermite interpolation

Authors

    • Institute of MathematicsJagiellonian University
Article

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 interpolationAlgebraic curves

Copyright information

© Springer-Verlag 2007