Abstract
A method is given to calculate exactly the stardiscrepancy of arbitrary finite plane sets. Using this method the stardiscrepancy of the sequences of Hammersley is obtained. The recursive structure of these sets allows for a proof by induction.
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De Clerck, L.: De exacte berekening van de sterdiscrepantie van de rijen van Hammerley in 2 dimensies. Ph. D. Thesis. Leuven. 1984.
Faure, H. Discrépance de suites associées à un système de numération (en dimension un). Bull. Soc. Math. France109, 143–182 (1981).
Faure, H.: Discrépance de suites associées à un système de numération (en dimensions). Acta Arith.XLI, 338–351 (1982).
Faure, H.: Suites à faible discrépance dansII s. Preprint.
Gabai, H.: On the discrepancy of certain sequences mod 1. Indag. Math.25, 603–605 (1963).
Halton, J. H.: On the efficiency of certain quasi-random sequences of points in evaluating multidimensional integrals. Numer. Math.2, 84–90; Berichtigung, ibid. Numer. Math. p. 196 (1960).
Halton, J. H., Zaremba, S. K.: The extreme and ℒ2-discrepancies of some plane sets. Mh. Math.73, 316–328 (1969).
Meijer, H. G.: The discrepancy of ag-adic sequence. Indag. Math.30, 54–66 (1968).
Niederreiter, H.: Discrepancy and convex programming. Ann. Mat. Pura Appl.93, 89–97 (1972).
Niederreiter, H.: Quasi-Monte Carlo methods and peudo-random numbers. Bull. Amer. Math. Soc.84, 957–1041 (1978).
Peart, P.: The dispersion of the Hammersley sequence in the unit square Mh. Math.94, 249–261 (1982).
White, B. E.: Mean-square discrepancies of the Hammersley and Zaremba sequences for arbitrary radix. Mh. Math.80, 219–229 (1975).
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De Clerck, L. A method for exact calculation of the stardiscrepancy of plane sets applied to the sequences of Hammersley. Monatshefte für Mathematik 101, 261–278 (1986). https://doi.org/10.1007/BF01559390
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DOI: https://doi.org/10.1007/BF01559390