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Discrépance et diaphonie en dimension un

Henri Chaix; Henri Faure

Acta Arithmetica (1993)

  • Volume: 63, Issue: 2, page 103-141
  • ISSN: 0065-1036

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Henri Chaix, and Henri Faure. "Discrépance et diaphonie en dimension un." Acta Arithmetica 63.2 (1993): 103-141. <http://eudml.org/doc/206510>.

@article{HenriChaix1993,
author = {Henri Chaix, Henri Faure},
journal = {Acta Arithmetica},
keywords = {-discrepancy; diaphony; generalized van der Corput sequences; explicit formulae},
language = {fre},
number = {2},
pages = {103-141},
title = {Discrépance et diaphonie en dimension un},
url = {http://eudml.org/doc/206510},
volume = {63},
year = {1993},
}

TY - JOUR
AU - Henri Chaix
AU - Henri Faure
TI - Discrépance et diaphonie en dimension un
JO - Acta Arithmetica
PY - 1993
VL - 63
IS - 2
SP - 103
EP - 141
LA - fre
KW - -discrepancy; diaphony; generalized van der Corput sequences; explicit formulae
UR - http://eudml.org/doc/206510
ER -

References

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  1. [1] E. Y. Atanassov, Note on the discrepancy of the van der Corput generalized sequences, C. R. Acad. Bulgare Sci. 42 (3) (1989), 41-44. Zbl0677.10038
  2. [2] E. Braaten and G. Weller, An improved low discrepancy sequence for multidimensional quasi-Monte-Carlo integration, J. Comput. Phys. 33 (1979), 249-258. Zbl0426.65001
  3. [3] H. Chaix et H. Faure, Discrépance et diaphonie des suites de van der Corput généralisées, C. R. Acad. Sci. Paris Sér. I Math. 310 (1990), 315-320. Zbl0694.10045
  4. [4] H. Chaix et H. Faure, Discrépance et diaphonie des suites de van der Corput généralisées (II), C. R. Acad. Sci. Paris Sér. I Math. 311 (1990), 65-68. Zbl0719.11045
  5. [5] H. Chaix et H. Faure, Discrépance et diaphonie des suites de van der Corput généralisées (III), C. R. Acad. Sci. Paris Sér. I Math. 312 (1991), 755-758. Zbl0743.11038
  6. [6] H. Faure, Discrépance de suites associées à un système de numération (en dimension un), Bull. Soc. Math. France 109 (1981), 143-182. Zbl0488.10052
  7. [7] H. Faure, Discrépance quadratique de la suite de van der Corput et de sa symétrique, Acta Arith. 55 (1990), 333-350. Zbl0705.11039
  8. [8] H. Faure, Good permutations for extreme discrepancy, J. Number Theory, à paraître. 
  9. [9] L. Kuipers and H. Niederreiter, Uniform Distribution of Sequences, Wiley, New York 1974. Zbl0281.10001
  10. [10] G. Pagès, Van der Corput sequences, Kakutani transforms and one-dimensional numerical integration, prépublication du CERMA, Ecole Nationale des Ponts et Chaussées, 1990. Zbl0765.41033
  11. [11] P. D. Proinov, Estimation of L²-discrepancy of a class of infinite sequences, C. R. Acad. Bulgare Sci. 36 (1) (1983), 37-40. 
  12. [12] P. D. Proinov, On irregularities of distribution, C. R. Acad. Bulgare Sci. 39 (9) (1986), 31-34. 
  13. [13] P. D. Proinov, Symmetrization of the van der Corput generalized sequences, Proc. Japan Acad. Ser. A Math. Sci. 64 (5) (1988), 159-162. 
  14. [14] P. D. Proinov and E. Y. Atanassov, On the distribution of the van der Corput generalized sequences, C. R. Acad. Sci. Paris Sér. I Math. 307 (1988), 895-900. Zbl0654.10051
  15. [15] P. D. Proinov and V. S. Grozdanov, Symmetrization of the van der Corput-Halton sequence, C. R. Acad. Bulgare Sci. 40 (8) (1987), 5-8. Zbl0621.10035
  16. [16] P. D. Proinov and V. S. Grozdanov, On the diaphony of the van der Corput-Halton sequence, J. Number Theory 30 (1988), 94-104. Zbl0654.10050
  17. [17] Y. J. Xiao, Suites équiréparties associées aux automorphismes du tore, C. R. Acad. Sci. Paris Sér. I Math. 311 (1990), 579-582. Zbl0713.11048
  18. [18] Y. J. Xiao, Contributions aux méthodes arithmétiques pour la simulation accélérée, Thèse, Ecole Nationale des Ponts et Chaussées, Septembre 1990. 
  19. [19] P. Zinterhof, Über einige Abschätzungen bei der Approximation von Funktionen mit Gleichverteilungsmethoden, Österreich. Akad. Wiss. Math.-Natur. Sitzungsber. II 185 (1976), 121-132. Zbl0356.65007
  20. [20] P. Zinterhof und H. Stegbuchner, Trigonometrische Approximation mit Gleichverteilungsmethoden, Studia Sci. Math. Hungar. 13 (1978), 273-289. Zbl0421.42001

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