Monatshefte für Mathematik

, Volume 102, Issue 2, pp 155–167 | Cite as

Low-discrepancy point sets

  • Harald Niederreiter
Article
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Abstract

Various point sets in thes-dimensional unit cube with small discrepancy are constructed.

Keywords

Small Discrepancy Unit Cube 
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References

  1. [1]
    Faure, H.: Discrépance de suites associées à un système de numération (en dimensions). Acta Arith.41, 337–351 (1982).Google Scholar
  2. [2]
    Hlawka, E.: Funktionen von beschränkter Variation in der Theorie der Gleichverteilung. Ann. Mat. Pura Appl.54, 325–333 (1961).Google Scholar
  3. [3]
    Hlawka, E.: Zur angenäherten Berechnung mehrfacher Integrale. Mh. Math.66, 140–151 (1962).Google Scholar
  4. [4]
    Hlawka, E.: Uniform distribution modulo 1 and numerical analysis. compositio Math.16, 92–105 (1964).Google Scholar
  5. [5]
    Hua, L.K., Wang, Y.: Applications of Number Theory to Numerical analysis. Berlin-Heidelberg-New York: Springer. 1981.Google Scholar
  6. [6]
    Korobov, N.M.: The approximate computation of multiple integrals. Dokl. Akad. Nauk SSSR124, 1207–1210 (1959) (Russian)Google Scholar
  7. [7]
    Larcher, G.: On the distribution of sequences connected with good lattice points. Mh. Math.101, 135–150 (1986).Google Scholar
  8. [8]
    Lidl, R., Niederreiter, H.: Finite fields. Reading: Addison-Wesley. 1983.Google Scholar
  9. [9]
    Niederreiter, H.: Pseudo-random numbers and optimal coefficients. Adv. in Math.26, 99–181 (1977).Google Scholar
  10. [10]
    Niederreiter, H.: Quasi-Monte Carlo methods and pseudo-random numbers. Bull. Amer. Math. Soc.84, 957–1041 (1978).Google Scholar
  11. [11]
    Niederreiter, H.: Multidimensional numerical integration using pseudorandom numbers. Proc. Numerical Methods for Stochastic Optimization (Laxenburg, 1983). Math. Programming Study27, 17–38. Amsterdam: North-Holland. (1986).Google Scholar
  12. [12]
    Niederreiter, H.: A statistical analysis of generalized feedback shift register pseudorandom number generators. SIAM J. Sci. Statist. Comp. (To appear.)Google Scholar
  13. [13]
    Niederreiter, H.: Pseudozufallszahlen und die Theorie der Gleichverteilung. Sitzungsber. Österr. akad. Wiss. Math.-Naturwiss. Kl. (To appear.)Google Scholar
  14. [14]
    Sobol', I.M.: Multidimensional Quadrature Formulas and Haar Functions. Moscow: Nauka. 1969. (Russian)Google Scholar

Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • Harald Niederreiter
    • 1
  1. 1.Kommission für MathematikÖsterreichische Akademie der WissenschaftenWienAustria

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