On convex approximation by quadratic splines
type: Item
instance of: scholarly article
title: On convex approximation by quadratic splines
zbMATH Open document ID: 0858.41015
published in: Journal of Approximation Theory
publication date: 1997-03-23T00:00:00Z
review text: This note is devoted to giving a short and constructive proof for the existence of a \(C^1\) convex quadratic spline with \(n\) equidistant knots which approximates a convex function \(f\in C[0,1]\) at the order \(\omega_3(f,1/n)\). This improves a result due to \textit{Y. K. Hu} [J. Approximation Theory 74, No. 1, 69-82 (1993; Zbl 0789.41005)], where the construction was much more complicated and the knots where only ``basically equidistant''. The authors end their note with a modified construction of a \(C^2\) convex cubic spline which provides the same degree of approximation. The ideas of this construction have since been extended by \textit{R. A. DeVore}, \textit{Y. K. Hu} and the reviewer [Constructive Approximation 12, No. 3, 409-422 (1996)] to convex approximation in the \(L_p\) norm.
Mathematics Subject Classification ID: 41A29
Mathematics Subject Classification ID: 41A25
Mathematics Subject Classification ID: 41A15
zbMATH DE Number: 885474
zbMATH Keywords: convex approximation by \(C'\) quadratic splines with equidistant knots
author: Kamen Ivanov
author: Bojan Popov
reviewed by: D. Leviatan
MaRDI profile type: Publication
full work available at URL: jath.1996.0032
OpenAlex ID: W2043063618
DOI: 10.1006/JATH.1996.0032
description: scientific article; zbMATH DE number 885474