ArticleOriginal scientific text

Title

General discrepancy estimates II: the Haar function system

Authors 1

Affiliations

  1. Institut für Mathematik, Universität Salzburg, Hellbrunner Strasse 34, A-5020 Salzburg, Austria

Keywords

discrepancy, Walsh functions, Haar functions, pseudorandom number generators, quasi-Monte Carlo methods

Bibliography

  1. J. Eichenauer-Herrmann, Inversive congruential pseudorandom numbers: a tutorial, Internat. Statist. Rev. 60 (1992), 167-176.
  2. P. Hellekalek, General discrepancy estimates: the Walsh function system, this volume, 209-218.
  3. L. Kuipers and H. Niederreiter, Uniform Distribution of Sequences, Wiley, New York, 1974.
  4. H. Niederreiter, Pseudo-random numbers and optimal coefficients, Adv. in Math. 26 (1977), 99-181.
  5. H. Niederreiter, Quasi-Monte Carlo methods and pseudo-random numbers, Bull. Amer. Math. Soc. 84 (1978), 957-1041.
  6. H. Niederreiter, New methods for pseudorandom number and pseudorandom vector generation, in: Proc. 1992 Winter Simulation Conference (Arlington, Va., 1992), IEEE Press, Piscataway, N.J., 1992, 264-269.
  7. H. Niederreiter, On a new class of pseudorandom numbers for simulation methods, J. Comput. Appl. Math., to appear.
  8. H. Niederreiter, Random Number Generation and Quasi-Monte Carlo Methods, SIAM, Philadelphia, 1992.
  9. F. Schipp, W. R. Wade, P. Simon and J. Pál, Walsh Series. An Introduction to Dyadic Harmonic Analysis, Adam Hilger, Bristol, 1990.
  10. I. M. Sobol', Multidimensional Quadrature Formulas and Haar Functions, Nauka, Moscow, 1969 (in Russian).
  11. I. M. Sobol' and O. V. Nuzhdin, A new measure of irregularity of distribution, J. Number Theory 39 (1991), 367-373.
Pages:
313-322
Main language of publication
English
Received
1993-05-21
Accepted
1994-03-07
Published
1994
Exact and natural sciences