Optimal recovery of isotropic classes of twice-differentiable multivariate functions
type: Item
instance of: scholarly article
title: Optimal recovery of isotropic classes of twice-differentiable multivariate functions
zbMATH Open document ID: 1215.41001
author: Sergiy Borodachov
author: Dmytro Skorokhodov
author: V. F. Babenko
published in: Journal of Complexity
publication date: 2010-12-01T00:00:00Z
review text: The authors consider functions defined on a convex body \(G\subset\mathbb R^d\), \(d\in\mathbb N\), i.e., a compact convex set with non-empty interior, and define two classes of functions. \(W_G\) is the class of continuously differentiable functions \(f:G\rightarrow\mathbb R\), such that the directional derivative of order \(2\) exists inside \(G\) for every direction (at least in a generalized sense) and has an essential supremum on \(G\) bounded by \(1\). \(\widetilde{W}_ {\mathcal L}\) is the class of \(\mathcal L\)-periodic continuous differentiable functions \(f:\mathbb R^d \rightarrow\mathbb R\), such that the directional derivative of order \(2\) exists on \(\mathbb R^d\) for every direction (at least in a generalized sense) and has an essential supremum on the fundamental parallelepiped, bounded by \(1\). Using the so-called central algorithm [c.f., \textit{J. F. Traub} and \textit{H. Wozniakowski}, A general theory of optimal algorithms. ACM Monograph Series. New York etc.: Academic Press (1980; Zbl 0441.68046)], the authors address three problems with respect to optimal recovery operators. The results are stated in 5 theorems (\S3) which are proved in \S\S5--9.
reviewed by: Marcel G. de Bruin
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 41A29
Mathematics Subject Classification ID: 52A20
zbMATH DE Number: 5822238
zbMATH Keywords: optimal recovery of functions
zbMATH Keywords: worst-case error
zbMATH Keywords: \(C^2\) functions
zbMATH Keywords: optimal covering
describes a project that uses: kepler98
MaRDI profile type: Publication
full work available at URL: j.jco.2010.07.004
OpenAlex ID: W2091233766
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DOI: 10.1016/J.JCO.2010.07.004
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description: scientific article; zbMATH DE number 5822238