Approximation to Data by Splines with Free Knots

descriptionPublicationkeyboard_double_arrow_right Article 01 Apr 1978 English Publisher:Society for Industrial & Applied Mathematics (SIAM)Journal:SIAM Journal on Numerical Analysis, volume 15, pages 328-343 (issn: 0036-1429, eissn: 1095-7170,

Copyright policy )

Authors: Jupp, David L. B.;

doi: 10.1137/0715022

Approximation to Data by Splines with Free Knots

- Summary
- Subjects
- Metrics

Abstract

Approximations to data by splines improve greatly if the knots are free variables. Using the B-spline representation for splines, and separating the linear and nonlinear aspects, the approximation problem reduces to nonlinear least squares in the variable knots.We describe the problems encountered in this formulation caused by the “lethargy” theorem, and how a logarithmic transformation of the knots can lead to an effective method for computing free knot spline approximations.

Keywords

Splines, Spline approximation, Lethargy Theorem, Effective Method For Computation, Splines with Free Knots, Nonlinear Least-Squares Formulation, Approximation of Data, Numerical computation using splines

Impact byBIP!

	selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	190
	popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.	Top 1%
	influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	Top 1%
	impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.	Average