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Improvement on the Discrepancy of (t, e, s)-Sequences Cover

Improvement on the Discrepancy of (t, e, s)-Sequences

Tatra Mountains Mathematical Publications
Volume 59 (2014): Issue 1 (June 2014)
By: Shu Tezuka  
Open Access
|Mar 2015

References

  1. [1] ATANASSOV, E. I.: On the discrepancy of the Halton sequences, Math. Balkanica (N.S.) 18 (2004), 15-32.
    Search in Google Scholar
  2. [2] BECK, J.: Probabilistic diophantine approximation,I.Kronecker sequences, Ann. of Math. 140 (1994), 109-160.10.2307/2118542
    Search in Google Scholar
  3. [3] DICK, J.-PILLICHSHAMMER, F.: Digital Nets and Sequences. Discrepancy Theory and Quasi-Monte Carlo Integration, Cambridge Univ. Press, Cambridge, 2010.10.1017/CBO9780511761188
    Search in Google Scholar
  4. [4] FAURE, H.: Discrépance de suites associées à un système de numération (en dimension s), Acta Arith. XLI (1982), 337-351.10.4064/aa-41-4-337-351
    Search in Google Scholar
  5. [5] FAURE, H.-KRITZER, P.: New star discrepancy bounds for (t, m, s)-nets and (t, s)- -sequences, Monatsh. Math. 172 (2013), 55-75.10.1007/s00605-012-0470-1
    Search in Google Scholar
  6. [6] FAURE, H.-LEMIEUX, C.: Improvements on the star discrepancy of (t, s)-sequences, Acta Arith. 154 (2012), 61-78.10.4064/aa154-1-4
    Search in Google Scholar
  7. [7] FAURE, H.-LEMIEUX, C.: Corrigendum to: “Improvements on the star discrepancy of (t, s)-sequences”, Acta Arith. 159 (2013), 299-300.10.4064/aa159-3-5
    Search in Google Scholar
  8. [8] FAURE, H.-LEMIEUX, C.: A variant of Atanassov’s method for (t, s)-sequences and (t, e, s)-sequences, J. Complexity 30 (2014), 620-633.10.1016/j.jco.2014.02.006
    Search in Google Scholar
  9. [9] HALTON, J. H.: On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals, Numer. Math. 2 (1960), 84-90.10.1007/BF01386213
    Search in Google Scholar
  10. [10] HOFER, R.-NIEDERREITER, H.: A construction of (t,s)-sequences with finite-row generating matrices using global function fields, Finite Fields Appl. 21 (2013), 97-110.10.1016/j.ffa.2012.11.004
    Search in Google Scholar
  11. [11] NIEDERREITER, H.: Point sets and sequences with small discrepancy, Monatsh. Math. 104 (1987), 273-337.10.1007/BF01294651
    Search in Google Scholar
  12. [12] NIEDERREITER, H.-YEO, A.: Halton-type sequences from global function fields, Sci. China Ser. A 56 (2013), 1467-1476.10.1007/s11425-013-4623-z
    Search in Google Scholar
  13. [13] SOBOL’, I. M.: The distribution of points in a cube and the approximate evaluation of integrals, U.S.S.R. Comput. Math. Math. Phys 7 (1967), 86-112; translation from Zh. Vychisl. Mat. Mat. Fiz. 7 (1967), 784-802.
    Search in Google Scholar
  14. [14] TEZUKA, S.: Polynomial arithmetic analogue of Halton sequences, ACM Trans. Model. Comput. Simul. 3 (1993), 99-107.10.1145/169702.169694
    Search in Google Scholar
  15. [15] TEZUKA, S.: Uniform Random Numbers: Theory and Practice, Kluwer Acad. Publ., Boston, 1995.10.1007/978-1-4615-2317-8
    Search in Google Scholar
  16. [16] TEZUKA, S.: On the discrepancy of generalized Niederreiter sequences, J. Complexity 29 (2013), 240-247.10.1016/j.jco.2013.02.001
    Search in Google Scholar
DOI: https://doi.org/10.2478/tmmp-2014-0016 | Journal eISSN: 1338-9750 | Journal ISSN: 12103195
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Language: English
Page range: 27 - 38
Submitted on: Jun 26, 2014
Published on: Mar 11, 2015
Published by: Slovak Academy of Sciences, Mathematical Institute
In partnership with: Paradigm Publishing Services
Publication frequency: 3 issues per year
Keywords:
low-discrepancy sequences,
signed splitting method,
(t,
e,
s)-sequences
Related subjects:
Mathematics,
General mathematics

© 2015 Shu Tezuka, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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