The exact exponent of sparse grid quadratures in the weighted case

Leszek Plaskota; Grzegorz W. Wasilkowski

doi:10.1006/jcom.2001.0598

The exact exponent of sparse grid quadratures in the weighted case

Leszek Plaskota, Grzegorz W. Wasilkowski

Computer Science

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

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. Woźniakowski (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.

Original language	English
Pages (from-to)	840-849
Number of pages	10
Journal	Journal of Complexity
Volume	17
Issue number	4
DOIs	https://doi.org/10.1006/jcom.2001.0598
State	Published - 2001

Bibliographical note

Funding Information:
1Partially supported by the State Committee for Scientific Research of Poland under Grant 2 P03A 00913. 2Partially supported by the National Science Foundation under Grant CCR-9729971.

ASJC Scopus subject areas

Algebra and Number Theory
Statistics and Probability
Numerical Analysis
General Mathematics
Control and Optimization
Applied Mathematics

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10.1006/jcom.2001.0598

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AB - 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. Woźniakowski (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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The exact exponent of sparse grid quadratures in the weighted case

Abstract

Bibliographical note

ASJC Scopus subject areas

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