The exponent of discrepancy of sparse grids is at least 2. 1933
type: Item
instance of: scholarly article
title: The exponent of discrepancy of sparse grids is at least 2. 1933
zbMATH Open document ID: 0947.65028
DOI: 10.1023/A:1018900715321
published in: Advances in Computational Mathematics
publication date: 2000-03-21T00:00:00Z
review text: The author examines bounds on the exponents of sparse grids for \(L_2\)-discrepancy and average case \(d\)-dimensional integration with respect to the Wiener sheet measure. He develops a technique that allows him not only lower bounds, but also upper bounds for exponents of sparse grids. The main result is that the minimal exponent of sparse grids for these problems is bounded from below by 2.1933.
Mathematics Subject Classification ID: 65D32
Mathematics Subject Classification ID: 65C05
zbMATH DE Number: 1419496
zbMATH Keywords: exponent of discrepancy
zbMATH Keywords: \(L_2\)-discrepancy
zbMATH Keywords: multivariate numerical integration
zbMATH Keywords: sparse grids
zbMATH Keywords: Smolyak's quadratures
zbMATH Keywords: Monte Carlo methods
author: Leszek Plaskota
reviewed by: Dumitru Acu
MaRDI profile type: Publication
full work available at URL: a:1018900715321
OpenAlex ID: W59382102
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description: scientific article; zbMATH DE number 1419496