Dyadic diaphony

Peter Hellekalek; Hannes Leeb

Acta Arithmetica (1997)

  • Volume: 80, Issue: 2, page 187-196
  • ISSN: 0065-1036

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Peter Hellekalek, and Hannes Leeb. "Dyadic diaphony." Acta Arithmetica 80.2 (1997): 187-196. <http://eudml.org/doc/207036>.

@article{PeterHellekalek1997,
author = {Peter Hellekalek, Hannes Leeb},
journal = {Acta Arithmetica},
keywords = {random number generators; weighted spectral test; diaphony; discrepancy; inequality of Erdős-Turán-Koksma; Weyl's Criterion; uniform distribution of sequences; pseudorandom number generation; dyadic diaphony; irregularity of the distribution of sequences; higher-dimensional unit cube; Weyl's criterion for the Walsh function system; inequality of Erdös-Turán-Koksma; Walsh spectral test; regular dyadic grids},
language = {eng},
number = {2},
pages = {187-196},
title = {Dyadic diaphony},
url = {http://eudml.org/doc/207036},
volume = {80},
year = {1997},
}

TY - JOUR
AU - Peter Hellekalek
AU - Hannes Leeb
TI - Dyadic diaphony
JO - Acta Arithmetica
PY - 1997
VL - 80
IS - 2
SP - 187
EP - 196
LA - eng
KW - random number generators; weighted spectral test; diaphony; discrepancy; inequality of Erdős-Turán-Koksma; Weyl's Criterion; uniform distribution of sequences; pseudorandom number generation; dyadic diaphony; irregularity of the distribution of sequences; higher-dimensional unit cube; Weyl's criterion for the Walsh function system; inequality of Erdös-Turán-Koksma; Walsh spectral test; regular dyadic grids
UR - http://eudml.org/doc/207036
ER -

References

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  2. [2] P. Hellekalek, General discrepancy estimates: the Walsh function system, Acta Arith. 67 (1994), 209-218. Zbl0805.11055
  3. [3] P. Hellekalek, Correlations between pseudorandom numbers: theory and numerical practice, in: P. Hellekalek, G. Larcher, and P. Zinterhof (eds.), Proc. 1st Salzburg Minisymposium on Pseudorandom Number Generation and Quasi-Monte Carlo Methods, Salzburg, 1994, volume ACPC/TR 95-4 of Technical Report Series, Austrian Center for Parallel Computation, University of Vienna, 1995, 43-73. 
  4. [4] P. Hellekalek and H. Niederreiter, The weighted spectral test: diaphony, in preparation, 1996. Zbl0921.11038
  5. [5] D. E. Knuth, The Art of Computer Programming, Vol. 2, Addison-Wesley, Reading, Mass., 1981. Zbl0477.65002
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  8. [8] B. D. Ripley, Stochastic Simulation, Wiley, New York, 1987. Zbl0613.65006
  9. [9] F. Schipp, W. R. Wade, and P. Simon (with the collaboration of J. Pál), Walsh Series. An Introduction to Dyadic Harmonic Analysis, Adam Hilger, Bristol, 1990. Zbl0727.42017
  10. [10] B. G. Sloss and W. F. Blyth, Walsh functions and uniform distribution mod 1, Tôhoku Math. J. 45 (1993), 555-563. Zbl0799.11020
  11. [11] S. Tezuka, Walsh-spectral test for GFSR pseudorandom numbers, J. Assoc. Comput. Mach. 30 (1987), 731-735. Zbl0632.65003
  12. [12] S. Tezuka, Uniform Random Numbers: Theory and Practice, Kluwer, Boston, 1995. Zbl0841.65004
  13. [13] P. Zinterhof, Über einige Abschätzungen bei der Approximation von Funktionen mit Gleichverteilungsmethoden, Sitzungsber. Österr. Akad. Wiss. Math.-Natur. Kl. II 185 (1976), 121-132. Zbl0356.65007
  14. [14] P. Zinterhof und H. Stegbuchner, Trigonometrische Approximation mit Gleichverteilungsmethoden, Studia Sci. Math. Hungar. 13 (1978), 273-289. Zbl0421.42001

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