Have a personal or library account? Click to login
An Improved Bound for the Star Discrepancy of Sequences in the Unit Interval Cover

An Improved Bound for the Star Discrepancy of Sequences in the Unit Interval

Open Access
|Jan 2017

References

  1. [1] FAURE, H.: Good permutations for extreme discrepancy, J. Number Theory 42 (1992), no. 1, 47–56.10.1016/0022-314X(92)90107-Z
  2. [2] KUIPERS, L.—NIEDERREITER, H.: Uniform Distribution of Sequences, John Wiley, New York, 1974.
  3. [3] LARCHER, G.: On the star discrepancy of sequences in the unit interval, J. Complexity 31 (2015), no. 3, 474–485.10.1016/j.jco.2014.07.005
  4. [4] LIARDET, P.: Discrepance sur le cercle, Primaths I, Univ. Marseille, 1979, 7–1.
  5. [5] NIEDERREITER, H.: Random Number Generation and Quasi-Monte Carlo Methods. In: CBMS-NSF Regional Conference Series in Applied Mathematics Vol. 63, SIAM, Philadelphia, 1992.10.1137/1.9781611970081
  6. [6] OSTROMOUKHOV, V.: Recent progress in improvement of extreme discrepancy and star discrepancy of one-dimensional sequences. In: Monte Carlo and quasi-Monte Carlo methods 2008, Springer, Berlin, 2009, pp. 561–572.10.1007/978-3-642-04107-5_36
  7. [7] SCHMIDT, W. M.: Irregularities of distribution, VII., Acta Arith. 21 (1972), 45–50.10.4064/aa-21-1-45-50
  8. [8] TIJDEMAN, R.—WAGNER, G.: A sequence has almost nowhere small discrepancy, Monatsh. Math. 90 (1980), no. 4, 315–329.
DOI: https://doi.org/10.1515/udt-2016-0001 | Journal eISSN: 2309-5377 | Journal ISSN: 1336-913X
Language: English
Page range: 1 - 14
Submitted on: Dec 1, 2014
Accepted on: Oct 2, 2015
Published on: Jan 13, 2017
Published by: Slovak Academy of Sciences, Mathematical Institute
In partnership with: Paradigm Publishing Services
Publication frequency: 2 issues per year

© 2017 Gerhard Larcher, Florian Puchhammer, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.