Computing Groebner bases of ideal interpolation
Commutative Algebra
2024-01-17 v2 Numerical Analysis
Numerical Analysis
Abstract
We present algorithms for computing the reduced Gr\"{o}bner basis of the vanishing ideal of a finite set of points in a frame of ideal interpolation. Ideal interpolation is defined by a linear projector whose kernel is a polynomial ideal. In this paper, we translate interpolation condition functionals into formal power series via Taylor expansion, then the reduced Gr\"{o}bner basis is read from formal power series by Gaussian elimination. Our algorithm has a polynomial time complexity. It compares favorably with MMM algorithm in single point ideal interpolation and some several points ideal interpolation.
Cite
@article{arxiv.2111.07340,
title = {Computing Groebner bases of ideal interpolation},
author = {Xue Jiang and Yihe Gong},
journal= {arXiv preprint arXiv:2111.07340},
year = {2024}
}
Comments
arXiv admin note: text overlap with arXiv:2007.11830