General discrepancy estimates II: the Haar function system

Peter Hellekalek

Acta Arithmetica (1994)

  • Volume: 67, Issue: 4, page 313-322
  • ISSN: 0065-1036

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Peter Hellekalek. "General discrepancy estimates II: the Haar function system." Acta Arithmetica 67.4 (1994): 313-322. <http://eudml.org/doc/206634>.

@article{PeterHellekalek1994,
author = {Peter Hellekalek},
journal = {Acta Arithmetica},
keywords = {discrepancy; Walsh functions; Haar functions; pseudorandom number generators; quasi-Monte Carlo methods; Erdős-Turán-Koksma inequality; pseudorandom number generation; Sobol's nonuniformity},
language = {eng},
number = {4},
pages = {313-322},
title = {General discrepancy estimates II: the Haar function system},
url = {http://eudml.org/doc/206634},
volume = {67},
year = {1994},
}

TY - JOUR
AU - Peter Hellekalek
TI - General discrepancy estimates II: the Haar function system
JO - Acta Arithmetica
PY - 1994
VL - 67
IS - 4
SP - 313
EP - 322
LA - eng
KW - discrepancy; Walsh functions; Haar functions; pseudorandom number generators; quasi-Monte Carlo methods; Erdős-Turán-Koksma inequality; pseudorandom number generation; Sobol's nonuniformity
UR - http://eudml.org/doc/206634
ER -

References

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  1. [1] J. Eichenauer-Herrmann, Inversive congruential pseudorandom numbers: a tutorial, Internat. Statist. Rev. 60 (1992), 167-176. Zbl0766.65002
  2. [2] P. Hellekalek, General discrepancy estimates: the Walsh function system, this volume, 209-218. Zbl0805.11055
  3. [3] L. Kuipers and H. Niederreiter, Uniform Distribution of Sequences, Wiley, New York, 1974. Zbl0281.10001
  4. [4] H. Niederreiter, Pseudo-random numbers and optimal coefficients, Adv. in Math. 26 (1977), 99-181. Zbl0366.65004
  5. [5] H. Niederreiter, Quasi-Monte Carlo methods and pseudo-random numbers, Bull. Amer. Math. Soc. 84 (1978), 957-1041. Zbl0404.65003
  6. [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. Zbl0849.11055
  7. [7] H. Niederreiter, On a new class of pseudorandom numbers for simulation methods, J. Comput. Appl. Math., to appear. Zbl0823.65010
  8. [8] H. Niederreiter, Random Number Generation and Quasi-Monte Carlo Methods, SIAM, Philadelphia, 1992. 
  9. [9] F. Schipp, W. R. Wade, P. Simon and J. Pál, Walsh Series. An Introduction to Dyadic Harmonic Analysis, Adam Hilger, Bristol, 1990. 
  10. [10] I. M. Sobol', Multidimensional Quadrature Formulas and Haar Functions, Nauka, Moscow, 1969 (in Russian). 
  11. [11] I. M. Sobol' and O. V. Nuzhdin, A new measure of irregularity of distribution, J. Number Theory 39 (1991), 367-373. Zbl0743.11039

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