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