Piecewise \(L\)-splines of order 4: interpolation and \(L^{2}\) error bounds for splines in tension
type: Item
instance of: scholarly article
title: Piecewise \(L\)-splines of order 4: interpolation and \(L^{2}\) error bounds for splines in tension
zbMATH Open document ID: 1181.41010
author: J. Blot
published in: Journal of Approximation Theory
publication date: 2010-01-08T00:00:00Z
review text: Piecewise L-splines are generalizations of L-splines in the sense that they satisfy different differential equations in different mesh intervals. The authors correct the erroneous results in [\textit{P. M. Prenter}, Numer. Math. 18, 243--253 (1971; Zbl 0227.65012)] for a certain family of piecewise L-splines of order 4. They prove existence and uniqueness and obtain the first and second integral relations. These results are used to obtain \(L^{2}\) error bounds for interpolation using splines in tension. Error bounds, for derivatives are also given.
reviewed by: Antonio López-Carmona
Mathematics Subject Classification ID: 41A15
Mathematics Subject Classification ID: 41A25
Mathematics Subject Classification ID: 65D05
zbMATH DE Number: 5655028
zbMATH Keywords: interpolation
zbMATH Keywords: piecewise \(L\)-splines
MaRDI profile type: Publication
full work available at URL: j.jat.2008.10.008
OpenAlex ID: W2019933135
cites work: Q5843703
cites work: Computation of Exponential Splines
cites work: Theory of exponential splines
cites work: Piecewise L-splines
cites work: Properties of splines in tension
cites work: Q4100478
cites work: L-splines
cites work: An Interpolation Curve Using a Spline in Tension
cites work: Exponential spline interpolation
DOI: 10.1016/J.JAT.2008.10.008
description: scientific article; zbMATH DE number 5655028