General discrepancy estimates: the Walsh function system

Peter Hellekalek

Acta Arithmetica (1994)

  • Volume: 67, Issue: 3, page 209-218
  • ISSN: 0065-1036

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Peter Hellekalek. "General discrepancy estimates: the Walsh function system." Acta Arithmetica 67.3 (1994): 209-218. <http://eudml.org/doc/206627>.

@article{PeterHellekalek1994,
author = {Peter Hellekalek},
journal = {Acta Arithmetica},
keywords = {discrepancy; Walsh functions; Vilenkin-Fourier series; pseudorandom number generators; quasi-Monte Carlo methods; pseudorandom numbers; Erdős Túran-Koksma inequality; generalized Walsh functions; extreme discrepancy; star discrepancy},
language = {eng},
number = {3},
pages = {209-218},
title = {General discrepancy estimates: the Walsh function system},
url = {http://eudml.org/doc/206627},
volume = {67},
year = {1994},
}

TY - JOUR
AU - Peter Hellekalek
TI - General discrepancy estimates: the Walsh function system
JO - Acta Arithmetica
PY - 1994
VL - 67
IS - 3
SP - 209
EP - 218
LA - eng
KW - discrepancy; Walsh functions; Vilenkin-Fourier series; pseudorandom number generators; quasi-Monte Carlo methods; pseudorandom numbers; Erdős Túran-Koksma inequality; generalized Walsh functions; extreme discrepancy; star discrepancy
UR - http://eudml.org/doc/206627
ER -

References

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  1. [1] T. Cochrane, On a trigonometric inequality of Vinogradov, J. Number Theory 27 (1987), 9-16. Zbl0629.10030
  2. [2] H. Niederreiter, On the distribution of pseudo-random numbers generated by the linear congruential method. III, Math. Comp. 30 (1976), 571-597. Zbl0342.65002
  3. [3] H. Niederreiter, Pseudo-random numbers and optimal coefficients, Adv. in Math. 26 (1977), 99-181. Zbl0366.65004
  4. [4] H. Niederreiter, Pseudozufallszahlen und die Theorie der Gleichverteilung, Sitzungsber. Österr. Akad. Wiss. Math.-Natur. Kl. II 195 (1986), 109-138. Zbl0616.10040
  5. [5] H. Niederreiter, Random Number Generation and Quasi-Monte Carlo Methods, SIAM, Philadelphia, 1992. 
  6. [6] F. Schipp, W. R. Wade, P. Simon and J. Pál, Walsh Series. An Introduction to Dyadic Harmonic Analysis, Adam Hilger, Bristol, 1990. 

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