Nearly optimal meshes in subanalytic sets
type: Item
instance of: scholarly article
title: Nearly optimal meshes in subanalytic sets
zbMATH Open document ID: 1323.32007
author: Wiesław Pleśniak
published in: Numerical Algorithms
publication date: 2012-11-01T00:00:00Z
review text: It is shown that nearly optimal meshes can be constructed on fat, compact, subanalytic subsets of \(\mathbb{R}^n\) that are known to admit certain Markov inequality [\textit{W. Pawłucki} and \textit{W. Pleśniak}, Math. Ann. 275, 467--480 (1986; Zbl 0579.32020)]. More precisely, the authors prove the following. Let \( K\) be a fat, compact, subanalytic subset of \(\mathbb{R}^n\). Then one can construct an admissible mesh \((A(d))\) on \(K\) such that \(\#A(d) = O((d \ln d)^N)\) as \(d\) tends to \(\infty\). In general, this provides better estimates of the cardinality of accessible meshes in subanalytic sets than those obtained by \textit{J.-P. Calvi} and \textit{N. Levenberg} [J. Approx. Theory 152, No. 1, 82--100 (2008; Zbl 1145.41001), Theorem 5].
reviewed by: H. P. Dikshit
Mathematics Subject Classification ID: 32B20
Mathematics Subject Classification ID: 41A10
Mathematics Subject Classification ID: 41A63
zbMATH DE Number: 6101121
zbMATH Keywords: admissible polynomial meshes
zbMATH Keywords: optimal meshes
zbMATH Keywords: subanalytic geometry
zbMATH Keywords: cardinality of accessible meshes
MaRDI profile type: Publication
full work available at URL: s11075-012-9578-6
OpenAlex ID: W1982669908
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DOI: 10.1007/S11075-012-9578-6
description: scientific article; zbMATH DE number 6101121