English

Polynomial interpolation in higher dimension: from simplicial complexes to GC sets

Classical Analysis and ODEs 2016-10-24 v1 Numerical Analysis

Abstract

Geometrically characterized (GC) sets were introduced by Chung-Yao in their work on polynomial interpolation in R^d. Conjectures on the structure of GC sets have been proposed by Gasca-Maeztu for the planar case, and in higher dimension by de Boor and Apozyan-Hakopian. We investigate GC sets in dimension three or more, and show that one way to obtain such sets is from the combinatorics of simplicial complexes.

Cite

@article{arxiv.1610.06851,
  title  = {Polynomial interpolation in higher dimension: from simplicial complexes to GC sets},
  author = {Nathan Fieldsteel and Hal Schenck},
  journal= {arXiv preprint arXiv:1610.06851},
  year   = {2016}
}

Comments

13 pages 2 figures

R2 v1 2026-06-22T16:27:55.581Z