×
White, Brian E.

Mean-square discrepancies of the Hammersley and Zaremba sequences for arbitrary radix. (English) Zbl 0322.65002

Monatsh. Math. 80, 219-229 (1975).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0322.65002

Cited in 1 Review
Cited in 9 Documents

MSC:

65C05 Monte Carlo methods
65D30 Numerical integration
11K38 Irregularities of distribution, discrepancy
Cite Review PDF
Full Text: DOI EuDML

References:

[1] Halton, J. H., andS. K. Zaremba: The extreme andL 2 discrepancies of some plane sets. Mh. Math.73, 316-328 (1969). · Zbl 0183.31401 · doi:10.1007/BF01298982
[2] Halton, J. H.: On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals. Num. Math.2, 84-90 (1960). · Zbl 0090.34505 · doi:10.1007/BF01386213
[3] Roth, K. F.: On irregularities of distribution. Mathematika1, 73-79 (1954). · Zbl 0057.28604 · doi:10.1112/S0025579300000541
[4] Halton, J. H.: A retrospective and prospective survey of the Monte Carlo method. SIAM Review12, 1-63 (1970). · Zbl 0193.46901 · doi:10.1137/1012001
[5] Warnock, T. T.: Computational Investigations of Low-Discrepancy Point Sets. Applications of Number Theory to Numerical Analysis, p. 319-343. New York: Academic Press. 1972.
[6] Halton, J. H.: Estimating the Accuracy of Quasi-Monte Carlo Integration. Applications of Number Theory to Numerical Analysis, p. 345-360. New York: Academic Press. 1972.
[7] Zaremba, S. K.: The mathematical basis of Monte Carlo and quasi-Monte Carlo methods. SIAM Review10, 303-314 (1968). · doi:10.1137/1010056
[8] Zaremba, S. K.: Good lattice points in the sense of Hlawka and Monte-Carlo integration. Mh. Math.72, 264-269 (1968). · Zbl 0195.19501 · doi:10.1007/BF01362552
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.