Quasi-Monte-Carlo methods and the dispersion of point sequences
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Publication:1921094
DOI10.1016/0895-7177(96)00036-2zbMath0855.11041OpenAlexW2035853071MaRDI QIDQ1921094
Publication date: 16 February 1997
Published in: Mathematical and Computer Modelling (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/0895-7177(96)00036-2
uniform distributionquasi-Monte Carlo methodsrange spacesdispersion of point sequencespolygonal approximation of curves
Monte Carlo methods (65C05) Numerical integration (65D30) Pseudo-random numbers; Monte Carlo methods (11K45)
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Uses Software
Cites Work
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- Point sets and sequences with small discrepancy
- On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals
- Funktionen von beschränkter Variation in der Theorie der Gleichverteilung
- Zur angenäherten Berechnung mehrfacher Integrale
- Über die isotrope Diskrepanz von Folgen. (On the isotropic discrepancy of sequences)
- The dispersion of a special sequence
- \(\epsilon\)-nets and simplex range queries
- C-uniform distribution on compact metric spaces
- Low-discrepancy and low-dispersion sequences
- An optimal visibility graph algorithm for triangulated simple polygons
- Almost tight bounds for \(\epsilon\)-nets
- Discrepancy and approximations for bounded VC-dimension
- Empty Simplices in Euclidean Space
- Algorithm 659
- Discrépance de suites associées à un système de numération (en dimension s)
- Multidimensional binary search trees used for associative searching
- Uniformly distributed sequences with an additional uniform property
- Localization of Search in Quasi-Monte Carlo Methods for Global Optimization
- Algorithm 647: Implementation and Relative Efficiency of Quasirandom Sequence Generators
- Implementation and tests of low-discrepancy sequences
- On the distribution of points in a cube and the approximate evaluation of integrals
- On the Uniform Convergence of Relative Frequencies of Events to Their Probabilities
