Free multivariate splines
type: Item
instance of: scholarly article
title: Free multivariate splines
zbMATH Open document ID: 0624.41012
DOI: 10.1007/BF01890567
author: Ronald DeVore
author: Vasil A. Popov
published in: Constructive Approximation
publication date: 1987-01-01T00:00:00Z
review text: An interesting type of nonlinear approximation is the univariate approximation by splines of a given degree, with a certain number of free knots. The word free here means that the knots are allowed to vary with the function being approximated; only the number of knots is held fixed. There has been no useful formulation of free knot splines in the case of several variables. The authors introduce a definition of multivariate free spline approximation, generalizing the univariate notion of spline with free knots. They give a characterization of certain approximation classes of functions, which have a prescribed order of approximation in \(L_ p\), in terms of the classical Besov spaces, in a way that is similar to the univariate case.
Mathematics Subject Classification ID: 41A15
Mathematics Subject Classification ID: 41A25
Mathematics Subject Classification ID: 41A63
Mathematics Subject Classification ID: 65D07
zbMATH DE Number: 4013218
zbMATH Keywords: univariate approximation
zbMATH Keywords: free spline approximation
zbMATH Keywords: Besov spaces
reviewed by: Dimitrie D. Stancu
MaRDI profile type: Publication
cites work: Q4066051
cites work: PIECEWISE-POLYNOMIAL APPROXIMATIONS OF FUNCTIONS OF THE CLASSES $ W_{p}^{\alpha}$
cites work: Q3797727
cites work: Interpolation of Besov Spaces
cites work: Russian text ignoredLp, 0 <p < 1
cites work: Q3739597
description: scientific article; zbMATH DE number 4013218