The jet of an interpolant on a finite set
type: Item
instance of: scholarly article
title: The jet of an interpolant on a finite set
zbMATH Open document ID: 1217.49024
DOI: 10.4171/RMI/639
author: Charles Fefferman
author: Arie Israel
published in: Revista Matemática Iberoamericana
publication date: 2011-05-03T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.rmi/1296828838
review text: Summary: We study functions \(F \in C^m(\mathbb R^n)\) having norm less than a given constant \(M\), and agreeing with a given function \(f\) on a finite set \(E\). Let \(\Gamma_f (S,M)\) denote the convex set formed by taking the \((m-1)\)-jets of all such \(F\) at a given finite set \(S \subset\mathbb R^n\). We provide an efficient algorithm to compute a convex polyhedron \(\widetilde{\Gamma}_f (S,M)\), such that \[ \Gamma_f (S,cM)\subset \widetilde{\Gamma}_f (S,M)\subset \Gamma_f (S,CM), \] where \(c\) and \(C\) depend only on \(m\) and \(n\).
Mathematics Subject Classification ID: 49K27
Mathematics Subject Classification ID: 52A35
Mathematics Subject Classification ID: 49M30
zbMATH DE Number: 5883110
zbMATH Keywords: interpolation
zbMATH Keywords: jet
zbMATH Keywords: algorithm
zbMATH Keywords: Whitney extension theorem
MaRDI profile type: Publication
cites work: A decomposition of multidimensional point sets with applications to k -nearest-neighbors and n -body potential fields
cites work: Fitting a \(C^m\)-smooth function to data. I.
cites work: Fitting a \(C^m\)-smooth function to data. III.
cites work: Fast Construction of Nets in Low-Dimensional Metrics and Their Applications
cites work: Q5566771
cites work: First draft of a report on the EDVAC
cites work: Q5607484
OpenAlex ID: W2013120029
description: scientific article; zbMATH DE number 5883110