The Set of Unattainable points for the Rational Hermite Interpolation Problem
Commutative Algebra
2017-10-03 v2 Algebraic Geometry
Abstract
We describe geometrically and algebraically the set of unattainable points for the Rational Hermite Interpolation Problem (i.e. those points where the problem does not have a solution). We show that this set is a union of equidimensional complete intersection varieties of odd codimension, the number of them being equal to the minimum between the degrees of the numerator and denominator of the problem. Each of these equidimensional varieties can be further decomposed as a union of as many rational (irreducible) varieties as input data points. We exhibit algorithms and equations defining all these objects.
Keywords
Cite
@article{arxiv.1704.08563,
title = {The Set of Unattainable points for the Rational Hermite Interpolation Problem},
author = {Cortadellas Teresa and D'Andrea Carlos and Montoro Eulalia},
journal= {arXiv preprint arXiv:1704.08563},
year = {2017}
}
Comments
22 pages, amsart. Revised version accepted for publication in Linear Algebra and its Applications