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

Nathan Fieldsteel; Hal Schenck

doi:10.1137/16M1057322

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

Nathan Fieldsteel
, Hal Schenck

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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

Original language	English (US)
Pages (from-to)	131-143
Number of pages	13
Journal	SIAM Journal on Numerical Analysis
Volume	55
Issue number	1
DOIs	https://doi.org/10.1137/16M1057322
State	Published - 2017

Keywords

Bi-Cohen Macaulay
Polynomial interpolation
Simplicial complex

ASJC Scopus subject areas

Numerical Analysis
Computational Mathematics
Applied Mathematics

Online availability

10.1137/16M1057322

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

keywords = "Bi-Cohen Macaulay, Polynomial interpolation, Simplicial complex",

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T1 - Polynomial interpolation in higher dimension

T2 - From simplicial complexes to GC sets

AU - Fieldsteel, Nathan

AU - Schenck, Hal

N1 - The work of the second author was supported by NSF 1312071.

PY - 2017

Y1 - 2017

N2 - Geometrically characterized (GC) sets were introduced by Chung and Yao in their work on polynomial interpolation in ℝd. Conjectures on the structure of GC sets have been proposed by Gasca and Maeztu for the planar case, and in higher dimension by de Boor and by Apozyan and Hakopian. We investigate GC sets in dimension three or higher, and show that one way to obtain such sets is from the combinatorics of simplicial complexes.

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

KW - Bi-Cohen Macaulay

KW - Polynomial interpolation

KW - Simplicial complex

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UR - https://www.scopus.com/pages/publications/85014502966#tab=citedBy

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JO - SIAM Journal on Numerical Analysis

JF - SIAM Journal on Numerical Analysis

IS - 1

ER -

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

Abstract

Keywords

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