Component-by-component construction of low-discrepancy point sets of small size
نویسندگان
چکیده
منابع مشابه
Construction of Low-Discrepancy Point Sets of Small Size by Bracketing Covers and Dependent Randomized Rounding
We provide a deterministic algorithm that constructs small point sets exhibiting a low star discrepancy. The algorithm is based on bracketing and on recent results on randomized roundings respecting hard constraints. It is structurally much simpler than the previous algorithm presented for this problem in [B. Doerr, M. Gnewuch, A. Srivastav. Bounds and constructions for the star discrepancy via...
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In a series of recent articles, such as, e.g., [5, 9, 16, 22], point sets mixed from integration node sets in different sorts of quasi-Monte Carlo rules have been studied. In particular, a finite version, based on Hammersley and lattice point sets, was introduced in [16], where the existence of such hybrid point sets with low star discrepancy was shown. However, up to now it has remained an ope...
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In [B. Doerr, M. Gnewuch, P. Kritzer, F. Pillichshammer. Monte Carlo Methods Appl., 14:129–149, 2008], a component-by-component (CBC) approach to generate small low-discrepancy samples was proposed and analyzed. The method is based on randomized rounding satisfying hard constraints and its derandomization. In this paper we discuss how to implement the algorithm and present first numerical exper...
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The standard method for constructing generating vectors for good lattice point sets is the componentby-component construction. Numerical experiments have shown that the generating vectors found by these constructions sometimes tend to have recurring components, which can lead to the problem of having projections with all lattice points lying on the main diagonal. In this paper we combine method...
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The class of (t,m, s)-nets and (t, s)-sequences, introduced in their most general form by Niederreiter, are important examples of point sets and sequences that are commonly used in quasi-Monte Carlo algorithms for integration and approximation. Low-dimensional versions of (t,m, s)-nets and (t, s)-sequences, such as Hammersley point sets and van der Corput sequences, form important sub-classes, ...
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ژورنال
عنوان ژورنال: Monte Carlo Methods and Applications
سال: 2008
ISSN: 0929-9629,1569-3961
DOI: 10.1515/mcma.2008.007