Spline Approximation Using Knot Density Functions

Andrew Crampton, Alistair B Forbes

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


This paper is concerned with the approximation of discrete data using univariate B-splines. Specifically, we focus on the need to locate spline knots optimally in order to improve the fidelity of the B-Spline model to the data. It is well understood that knot placement can have a significant effect on the quality of a spline approximant. However optimizing with respect to the number and placement of knots is generally difficult. In this paper, we describe an approach in which the density of knots is controlled by a knot density function depending on a small number of parameters. Optimizing with respect to these additional parameters is straightforward and can lead to significant improvements in the approximating spline.
Original languageEnglish
Title of host publicationAlgorithms for Approximation
Subtitle of host publicationProceedings of the 5th International Conference, Chester, July 2005
EditorsArmin Iske, Jeremy Levesley
Place of PublicationBerlin
Number of pages10
ISBN (Electronic)9783540465515
ISBN (Print)9783540332831, 9783642069949
Publication statusPublished - 2007
Event5th International Conference on Algorithms for Approximation - Chester, United Kingdom
Duration: 17 Jul 200521 Jul 2005
Conference number: 5


Conference5th International Conference on Algorithms for Approximation
Country/TerritoryUnited Kingdom


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