Three-monotone spline approximation
type: Item
instance of: scholarly article
title: Three-monotone spline approximation
zbMATH Open document ID: 1208.41004
author: G. A. Dzyubenko
author: Kirill A. Kopotun
author: A. V. Prymak
published in: Journal of Approximation Theory
publication date: 2011-01-21T00:00:00Z
review text: Jackson theorems for functions \(f\) whose third order divided differences are always nonnegative are studied. They are approximated by piecewise polynomial splines with minimal defect, and the error is bounded above in a Jackson-type theorem using the fourth modulus of smoothness of \(f\). Such functions are called three-monotone, and so is the spline which is used as an approximation. The error-estimate is in the uniform norm. Analogous results are provided using the Ditzian-Totik modulus of smoothness. They also hold in the uniform norm (and not in other \(p\)-norms, \(p\) finite, so long as the knots of the approximating spline are independent of \(f\)).
reviewed by: Martin D. Buhmann
Mathematics Subject Classification ID: 41A15
zbMATH DE Number: 5840441
zbMATH Keywords: 3-monotone approximation by piecewise polynomials and splines
zbMATH Keywords: degree of approximation
zbMATH Keywords: Jackson-type estimates
MaRDI profile type: Publication
full work available at URL: j.jat.2010.07.004
OpenAlex ID: W1975857851
cites work: Restricted Range Approximation by Splines and Variational Inequalities
cites work: Negative results in form-preserving approximation of higher order
cites work: Shape preserving widths of Sobolev-type classes of \(s\)-monotone functions on a finite interval.
cites work: Univariate splines: Equivalence of moduli of smoothness and applications
cites work: Nearly monotone spline approximation in 𝕃_{𝕡}
cites work: Constrained Spline Smoothing
cites work: On k-Monotone Approximation by Free Knot Splines
cites work: On 3-monotone approximation by piecewise polynomials
cites work: Convex functions, partial orderings, and statistical applications
cites work: Three-convex approximation by free knot splines in \(C[0,1]\)
cites work: Another Proof that Convex Functions are Locally Lipschitz
cites work: Q3913213
DOI: 10.1016/J.JAT.2010.07.004
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description: scientific article; zbMATH DE number 5840441