The sensitivity of a spline function to perturbations of the knots
type: Item
instance of: scholarly article
title: The sensitivity of a spline function to perturbations of the knots
zbMATH Open document ID: 0927.41007
DOI: 10.1023/A:1022346030560
author: Tom Lyche
author: Knut Mørken
published in: BIT
publication date: 1999-12-07T00:00:00Z
review text: The authors study the bounds for the difference between a primary spline and a secondary spline with the same B-spline coefficients, but different knots. It is shown that a continuous spline and its derivatives depend continuously on the knots in any \(L^p\)-space, \(p \geq 1\), while a discontinuous spline is only Lipshitz continuous with exponent \({1} \over {p}\) in \(L^p\). The authors also show that the results can be extended for parametric spline curves.
reviewed by: H. P. Dikshit
Mathematics Subject Classification ID: 41A15
zbMATH DE Number: 1309455
zbMATH Keywords: B-splines
zbMATH Keywords: divided differences
zbMATH Keywords: perturbation of knots
MaRDI profile type: Publication
full work available at URL: a:1022346030560
OpenAlex ID: W2138914717
description: scientific article; zbMATH DE number 1309455