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The Exact Exponent of Sparse Grid Quadratures in the Weighted Case

✍ Scribed by Leszek Plaskota; Grzegorz W. Wasilkowski

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 111 KB
Volume: 17
Category: Article
ISSN: 0885-064X
DOI: 10.1006/jcom.2001.0598

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✦ Synopsis

This paper provides a lower bound on the exponent of tractability for Sparse Grid Quadratures for multivariate integration of functions from a certain class of weighted tensor product spaces. This lower bound is sharp since it matches a corresponding upper bound of G. W. Wasilkowski and H. Woz ´niakowski (1999, J. Complexity 15, 402-447). It also shows that, for slowly decreasing weights, the exponent of Sparse Grid Quadratures is far from being optimal.

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