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The extreme and L2 discrepancies of some plane sets

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References

  1. Davenport, H.: Note on irregularities of distribution. Mathematika3, 131–135 (1956).

    Google Scholar 

  2. Gabai, H.: On the discrepancy of certain sequences mod 1. Indag. Math.25, 603–605 (1963).

    Google Scholar 

  3. Halton, J. H.: On the efficiency of certain quasi-random sequences of points in evaluating multidimensional integrals. Numer. Math.2, 84–90 and 196 (1960).

    Google Scholar 

  4. Halton, J. H.: A retrospective and prospective survey of the Monte Carlo method, SIAM Rev. (to appear).

  5. Hlawka, E.: Funktionen von beschränkter Variation in der Theorie der Gleichverteilung. Ann. Mat. Pura App. (iv)54, 325–334 (1961).

    Google Scholar 

  6. Roth, K. F.: On irregularities of distribution. Mathematika1, 73 bis 79 (1954).

    Google Scholar 

  7. Zaremba, S. K.: The mathematical basis of Monte Carlo and quasi-Monte Carlo methods. SIAM Rev.10, 303–314 (1968).

    Google Scholar 

  8. Zaremba, S. K.: Some applications of multidimensional integration by parts. Ann. Polon. Math.21, 85–96 (1969).

    Google Scholar 

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Author notes

  1. J. H. Halton

    Present address: Computer Sciences Dept., University of Wisconsin, 1210, West Dayton Street, 53706, Madison, Wis., USA

  2. S. K. Zaremba

    Present address: Centre de recherches Mathématiques, Université de Montréal, Case postale 6128, Montréal 3, Canada

Authors and Affiliations

  1. Universita of Wales, Swansea

    J. H. Halton & S. K. Zaremba

Authors
  1. J. H. Halton
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  2. S. K. Zaremba
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Additional information

The authors acknowledge the partial support of the U.S. Army at the Mathematics Research Center, under Contract No. DA-31-124-ARO-D-462, and also (J.H.H.) that of the National Science Foundation, under Grant No. GJ-171, in the preparation of this paper.

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Halton, J.H., Zaremba, S.K. The extreme and L2 discrepancies of some plane sets. Monatshefte für Mathematik 73, 316–328 (1969). https://doi.org/10.1007/BF01298982

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