Uniform B-spline approximation in Sobolev spaces
type: Item
instance of: scholarly article
title: Uniform B-spline approximation in Sobolev spaces
zbMATH Open document ID: 0890.65012
DOI: 10.1023/A:1019250217452
author: U. Reif
published in: Numerical Algorithms
publication date: 1997-12-11T00:00:00Z
review text: The author presents a new method for approximating functions by uniform B-splines, which is based on the orthogonality relations for those splines in weighted Sobolev spaces. The approximating spline only depends on the local shape of the given function, and the approximation order is optimal. The solution of a constrained approximation problem is simply obtained by first solving the unconstrained problem and then projecting the control points on the feasible set. Furthermore, the approximation scheme is applied to the problems of knot removal and degree reduction.
Mathematics Subject Classification ID: 65D07
Mathematics Subject Classification ID: 65D15
Mathematics Subject Classification ID: 41A15
zbMATH DE Number: 1078347
zbMATH Keywords: spline conversion
zbMATH Keywords: uniform B-splines
zbMATH Keywords: Sobolev spaces
zbMATH Keywords: control points
zbMATH Keywords: knot removal
zbMATH Keywords: degree reduction
reviewed by: Johannes Elschner
MaRDI profile type: Publication
full work available at URL: a:1019250217452
OpenAlex ID: W2192978065
description: scientific article; zbMATH DE number 1078347