Tractability of multivariate integration for weighted Korobov classes
type: Item
instance of: scholarly article
title: Tractability of multivariate integration for weighted Korobov classes
zbMATH Open document ID: 0998.65004
author: Ian H. Sloan
author: H. Woźniakowski
published in: Journal of Complexity
publication date: 2002-07-02T00:00:00Z
review text: The authors study the worst case error of multivariate integration in weighted Korobkov classes of periodic functions of \(d\)~coordinates. These classes are defined in terms of weights which moderate the behavior of functions with respect to successive coordinates. Two classes of quadrature rules are studied, i.e., the quasi Monte Carlo rules which use \(n\) function values and in which all quadrature weights are \(1/n\) and rules for which all quadrature weights are non-negative. The tractability and strong tractability results are achieved under the relatively small class of lattice rules. The authors also check how the randomized error of the (classical) Monte Carlo algorithm depends on~\(d\) for weighted Korobkov classes.
Mathematics Subject Classification ID: 65C05
Mathematics Subject Classification ID: 65Y20
Mathematics Subject Classification ID: 65D32
Mathematics Subject Classification ID: 41A55
zbMATH DE Number: 1736576
zbMATH Keywords: multivariate integration
zbMATH Keywords: Korobkov classes
zbMATH Keywords: quadrature rules
zbMATH Keywords: quasi Monte Carlo methods
zbMATH Keywords: Monte Carlo methods
zbMATH Keywords: strong tractability
zbMATH Keywords: worst case error
zbMATH Keywords: periodic function
reviewed by: Jaromír Antoch
MaRDI profile type: Publication
full work available at URL: jcom.2001.0599
OpenAlex ID: W2092549287
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DOI: 10.1006/JCOM.2001.0599
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description: scientific article; zbMATH DE number 1736576