Aitken-Neville sets, principal lattices and divided differences
type: Item
instance of: scholarly article
title: Aitken-Neville sets, principal lattices and divided differences
zbMATH Open document ID: 1162.65003
author: M. Gasca
author: J. M. Carnicer
author: Tomas Sauer
published in: Journal of Approximation Theory
publication date: 2009-03-30T00:00:00Z
review text: The multivariate polynomial interpolation is related to generalized principal lattices. It is shown that any generalized principal lattice is an Aitken-Neville configuration (and so can be evaluated by iterated linear interpolation). The converse will be shown for dimension 2 and \(dg\geq3\). The divided differences, associated to Aitken-Neville configuration are considered and their spline representation is derived.
reviewed by: Ljubiša Kocić
Mathematics Subject Classification ID: 65D05
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 41A15
Mathematics Subject Classification ID: 41A63
zbMATH DE Number: 5534943
zbMATH Keywords: polynomial interpolation
zbMATH Keywords: principal lattice
zbMATH Keywords: Aitken-Neville set
zbMATH Keywords: divided difference
zbMATH Keywords: multivariate
zbMATH Keywords: Aitken-Neville configuration
zbMATH Keywords: iterated linear interpolation
zbMATH Keywords: spline representation
MaRDI profile type: Publication
full work available at URL: j.jat.2008.04.019
OpenAlex ID: W2133957845
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DOI: 10.1016/J.JAT.2008.04.019
description: scientific article; zbMATH DE number 5534943