The Discrepancy and Gain Coefficients of Scrambled Digital Nets
نویسندگان
چکیده
منابع مشابه
The Discrepancy of Digital Nets
Digital sequences and nets are among the most popular kinds of low discrepancy sequences and are often used for quasi-Monte Carlo quadrature rules. Several years ago Owen proposed a method of scrambling digital sequences and recently Faure and Tezuka have proposed another method. This article considers the discrepancy of digital nets under these scramblings. The first main result of this articl...
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Digital nets are very important representatives in the family of lowdiscrepancy point sets which are often used as underlying nodes for quasi-Monte Carlo integration rules. Here we consider a special sub-class of digital nets known as cyclic nets and, more general, hyperplane nets. We show the existence of such digital nets of good quality with respect to star discrepancy in the classical as we...
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We introduce a new construction method for digital nets which yield point sets in the s-dimensional unit cube with small star discrepancy. The digital nets are constructed using polynomials over finite fields. It has long been known that there exist polynomials which yield point sets with small (unweighted) star discrepancy. This result was obtained by Niederreiter by the means of averaging ove...
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[0,1]d f(x)dx. Monte Carlo (MC) sampling typically attains a root mean squared error (RMSE) of O(n) from n independent random function evaluations. By contrast, quasi-Monte Carlo (QMC) sampling using carefully equispaced evaluation points can attain the rate O(n) for any ε > 0 and randomized QMC (RQMC) can attain the RMSE O(n), both under mild conditions on f . Classical variance reduction meth...
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This paper deals with a recent modification of the Monte Carlo method known as quasi random Monte Carlo. Under this approach, one uses specially selected deterministic sequences rather than random sequences as in Monte Carlo. These special sequences are known as low discrepancy sequences and have the property that they tend to be evenly dispersed throughout the unit cube. For many applications ...
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ژورنال
عنوان ژورنال: Journal of Complexity
سال: 2002
ISSN: 0885-064X
DOI: 10.1006/jcom.2001.0630