On the approximation properties of nonsmooth convex disks
type: Item
instance of: scholarly article
title: On the approximation properties of nonsmooth convex disks
zbMATH Open document ID: 1007.52003
published in: Computational Mathematics and Mathematical Physics
publication date: 2003-03-12T00:00:00Z
review text: The author examines the accuracy of approximation of two-dimensional convex compact bodies by polygons. The well-known upper bounds on approximation accuracy are determined by \(\sim\;c/n^2\), where \(n\) is the number of vertices of the polygon. The goal of this work is to obtain a constructive upper bound on theaccuracy for nonsmooth bodies permitting a higher convergence rate then \(c/n^2\). An algorithm is constructed, for which a stronger bound is obtained for nonsmooth bodies.
Mathematics Subject Classification ID: 52A27
Mathematics Subject Classification ID: 52A40
Mathematics Subject Classification ID: 52A37
zbMATH DE Number: 1779315
zbMATH Keywords: approximation
zbMATH Keywords: convex bodies
zbMATH Keywords: polygon
zbMATH Keywords: upper bounds
zbMATH Keywords: convergence rate
zbMATH Keywords: accuracy
zbMATH Keywords: vertices
zbMATH Keywords: algorithm
zbMATH Keywords: nonsmooth
author: G. K. Kamenev
reviewed by: A. Tret'yakov
MaRDI profile type: Publication
Recommended article: Approximation on Disks
Recommended article: Q3687162
Recommended article: Q3761046
Recommended article: Q4696463
Recommended article: Approximation of convex discs by polygons
Recommended article: Continuity and convergence properties of extremal-interpolating disks
Recommended article: Approximate fixed point property and unions of convex disks in the digital plane
Recommended article: Abstract convex approximations of nonsmooth functions
Recommended article: Approximation of general smooth convex bodies
Recommended article: On properties of discretized convex curves
description: scientific article; zbMATH DE number 1779315