Characterization of Generalized Lipschitz Classes by Best Approximation with Splines

descriptionPublicationkeyboard_double_arrow_right Article 01 Apr 1974 English Publisher:Society for Industrial & Applied Mathematics (SIAM)Journal:SIAM Journal on Numerical Analysis, volume 11, pages 283-304 (issn: 0036-1429, eissn: 1095-7170,

Copyright policy )

Authors: Scherer, Karl;

doi: 10.1137/0711027

Characterization of Generalized Lipschitz Classes by Best Approximation with Splines

- Summary
- Subjects
- Metrics

Abstract

Equivalence theorems for best approximation by splines with equidistant nodes on a finite interval are established. They yield characterizations of the generalized Lipschitz spaces $(\omega _r (t,f)_p $ being the rth modulus of continuity) \[ Lip(\psi ,q,r;p) = \{ f \in L_p (a,b):\left\{ {\begin{array}{*{20}c} {\int_0^1 {[\psi ^{ - 1} (t)\omega _r (t,f)_p ]^q {{dt} / {t 0$ is non-decreasing, an aspect not covered by pr...

Keywords

Spline approximation, Numerical interpolation, Numerical smoothing, curve fitting

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).	11
	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.	Average
	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 10%
	impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.	Top 10%