On Corner Avoidance Properties of Random‐Start Halton Sequences
نویسندگان
چکیده
منابع مشابه
On Corner Avoidance Properties of Random-Start Halton Sequences
Recently, the analysis of quasi-Monte Carlo (QMC) sampling of integrands with singularities gained considerable interest. In this setting error bounds for QMC integration, in addition to discrepancy, include a measure how well the singularities are avoided by the utilized sequences. The article aims to generalize results for the corner avoidance of the classical Halton sequence to Halton sequen...
متن کاملA note on corner avoidance of random-start Halton sequences
Recently, the analysis of quasi-Monte Carlo (QMC) sampling of integrands with singularities gained considerable interest. In this setting error bounds for QMC integration, in addition to discrepancy, include a measure how well the singularities are avoided by the utilized sequences. The article aims to generalize results for the corner avoidance of the classical Halton sequence to Halton sequen...
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The minimum distance of QMC sample points to the boundary of the unit cube is an important quantity in the error analysis of QMC integration for functions with singularities. Sobol’ and recently Owen show that the Sobol’ and Halton sequences avoid a hyperbolically shaped region around the corners of the unit cube. We extend these results in two ways. First, we prove that generalized Niederreite...
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We investigate a parametric extension of the classical s-dimensional Halton sequence, where the bases are special Pisot numbers. In a onedimensional setting the properties of such sequences have already been investigated by several authors [5, 8, 23, 28]. We use methods from ergodic theory to in order to investigate the distribution behavior of multidimensional versions of such sequences. As a ...
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Halton’s low discrepancy sequence is still very popular in spite of its shortcomings with respect to the correlation between points of two-dimensional projections for large dimensions. As a remedy, several types of scrambling and/or randomizations for this sequence have been proposed. We examine empirically some of these by calculating their L4and L2-discrepancies (D* resp. T*), and by performi...
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ژورنال
عنوان ژورنال: SIAM Journal on Numerical Analysis
سال: 2007
ISSN: 0036-1429,1095-7170
DOI: 10.1137/050645361