Sequential algorithms of optimal order global error for the uniform recovery of functions with monotone (r-1) derivatives
type: Item
instance of: scholarly article
title: Sequential algorithms of optimal order global error for the uniform recovery of functions with monotone (r-1) derivatives
zbMATH Open document ID: 0577.65002
DOI: 10.1007/BF01904781
author: Gy. Sonnevend
published in: Analysis Mathematica
publication date: 1984-01-01T00:00:00Z
review text: Seien \(r\in {\mathbb{N}}\), \(r\geq 2\), \(a=\tau_ 1\leq \tau_ 2\leq...\leq \tau_{r+1}=b\), \(K^ 0:=\{z| z(\tau_ i)=x(\tau_ i)\), \(i=1,...,r+1\); \(z^{(r-1)}\) monoton nicht abnehmend in [a,b]\(\}\) und \(x\in K^ 0\) die zu approximierende Funktion. Es wird eine Klasse sequentieller Algorithmen zur Wahl von Knoten \(t_ 1,...,t_ N\) und hiermit erzeugter Approximationen an x bezüglich \(K^ 0\) kontruiert. Nach Einführung geeigneter individueller und globaler Fehlerbegriffe wird gezeigt, daß diese adaptiven Verfahren in einem bestimmten Sinn (Ordnung in N) besser sind als ''passive'' Verfahren mit simultaner Knotenwahl.
Mathematics Subject Classification ID: 65D05
Mathematics Subject Classification ID: 65D07
Mathematics Subject Classification ID: 41A25
Mathematics Subject Classification ID: 41A29
zbMATH DE Number: 3923937
zbMATH Keywords: optimal order global error
zbMATH Keywords: uniform recovery of functions
zbMATH Keywords: sequential algorithms
zbMATH Keywords: adaptive algorithms
zbMATH Keywords: monotone derivatives
MaRDI profile type: Publication
cites work: A practical guide to splines.
cites work: An adaptive algorithm for multivariate approximation giving optimal convergence rates
cites work: Piecewise polynomial approximation on optimal meshes
cites work: Best choice of knots in approximation of functions by local Hermitian splines
cites work: Q4156369
cites work: Q3900444
cites work: Q3889993
cites work: Q3882291
cites work: Necessary and sufficient conditions for interpolation with functions having monotone r-th derivatives
cites work: Q3922550
cites work: An optimal sequential algorithm for the uniform approximation of convex functions on \([0,1]^ 2\)
cites work: Q3883494
description: scientific article; zbMATH DE number 3923937