An explicit construction of optimal order quasi-Monte Carlo rules for smooth integrands (Q2817786)
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scientific article; zbMATH DE number 6621954
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An explicit construction of optimal order quasi-Monte Carlo rules for smooth integrands |
scientific article; zbMATH DE number 6621954 |
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2 September 2016
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quasi-Monte Carlo
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numerical integration
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higher-order digital nets
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Sobolev space
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kernel Hilbert space
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worst case error
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An explicit construction of optimal order quasi-Monte Carlo rules for smooth integrands (English)
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The authors consider quasi-Monte Carlo (QMC) rules for numerical integration in a reproducing kernel Hilbert space. An explicit construction of an optimal QMC rule is presented. The approach depends on digital nets and the construction of Chen and Skriganov. The main result gives an upper bound for the worst case error which is of the order NEWLINE\[NEWLINEO(\frac{(\log N)^{\frac{s-1}{2}}}{N^{\alpha}}),NEWLINE\]NEWLINE where \(s\) is the dimension and \(\alpha\) the order of smoothness.
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