English

Subresultants, Sylvester sums and the rational interpolation problem

Commutative Algebra 2014-03-25 v3

Abstract

We present a solution for the classical univariate rational interpolation problem by means of (univariate) subresultants. In the case of Cauchy interpolation (interpolation without multiplicities), we give explicit formulas for the solution in terms of symmetric functions of the input data, generalizing the well-known formulas for Lagrange interpolation. In the case of the osculatory rational interpolation (interpolation with multiplicities), we give determinantal expressions in terms of the input data, making explicit some matrix formulations that can independently be derived from previous results by Beckermann and Labahn.

Keywords

Cite

@article{arxiv.1211.6895,
  title  = {Subresultants, Sylvester sums and the rational interpolation problem},
  author = {Carlos D'Andrea and Teresa Krick and Agnes Szanto},
  journal= {arXiv preprint arXiv:1211.6895},
  year   = {2014}
}

Comments

14 pages, revised version accepted for publication in the Journal of Symbolic Computation

R2 v1 2026-06-21T22:46:05.575Z