Local Lagrange interpolation using cubic \(C^{1}\) splines on type-4 cube partitions
type: Item
instance of: scholarly article
title: Local Lagrange interpolation using cubic \(C^{1}\) splines on type-4 cube partitions
zbMATH Open document ID: 1193.41009
author: Michael A. Matt
author: Günther Nürnberger
published in: Journal of Approximation Theory
publication date: 2010-05-11T00:00:00Z
review text: Continuously differentiable, piecewise cubic splines are studied in three dimensions. A local Lagrange interpolation method is analysed and shown to be stable and to have optimal approximation order. Moreover, it has linear complexity. An implementation of the method is discussed in detail, and numerical results are provided too.
reviewed by: Martin D. Buhmann
Mathematics Subject Classification ID: 41A15
Mathematics Subject Classification ID: 41A05
zbMATH DE Number: 5706945
zbMATH Keywords: trivariate splines
zbMATH Keywords: Lagrange interpolation
zbMATH Keywords: type-4 partitions
MaRDI profile type: Publication
full work available at URL: j.jat.2009.07.009
OpenAlex ID: W2044671404
cites work: Smooth macro-elements based on Clough-Tocher triangle splits
cites work: Q4300595
cites work: A local Lagrange interpolation method based on $C^{1}$ cubic splines on Freudenthal partitions
cites work: Spline Functions on Triangulations
cites work: Lagrange interpolation by bivariate \(C^1\)-splines with optimal approximation order
cites work: Q3154840
cites work: Lagrange interpolation by \(C^1\) cubic splines on triangulated quadrangulations
cites work: Q5465293
cites work: Local Lagrange interpolation with bivariate splines of arbitrary smoothness
cites work: \(C^1\) quintic splines on type-4 tetrahedral partitions
cites work: A Markov inequality in several dimensions
cites work: An \(n\)-dimensional Clough-Tocher interpolant
DOI: 10.1016/J.JAT.2009.07.009
Recommended article: Local Lagrange interpolation with cubic \(C^{1}\) splines on tetrahedral partitions
Recommended article: A local Lagrange interpolation method based on $C^{1}$ cubic splines on Freudenthal partitions
Recommended article: Local Lagrange interpolation by bivariate \(C^1\) cubic splines
Recommended article: Local quasi-interpolation by cubic C1 splines on type-6 tetrahedral partitions
Recommended article: Q4825584
Recommended article: Local Lagrange interpolation by quintic \(C^1\) splines on type-6 tetrahedral partitions
Recommended article: A Lagrange Interpolation Method by Trivariate Cubic C 1 Splines of Low Locality
Recommended article: Q3480653
Recommended article: Lagrange interpolation by \(C^1\) cubic splines on triangulated quadrangulations
Recommended article: Q5432226
description: scientific article; zbMATH DE number 5706945