## Error estimates arising from certain pseudorandom sequences in a quasirandom search method

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- by Ricardo A. Mitchell PDF
- Math. Comp.
**55**(1990), 289-297 Request permission

## Abstract:

In this paper we apply number-theoretic results to estimate the dispersion, a measure of denseness for sequences in a bounded set, of the Halton and Hammersley sequences in the hypercube ${I^s} = {[0,1]^s}$. It is seen that they attain the minimal order of magnitude for the dispersion.## References

- H. Niederreiter,
*A quasi-Monte Carlo method for the approximate computation of the extreme values of a function*, Studies in pure mathematics, Birkhäuser, Basel, 1983, pp. 523–529. MR**820248** - Harald Niederreiter,
*Quasi-Monte Carlo methods and pseudo-random numbers*, Bull. Amer. Math. Soc.**84**(1978), no. 6, 957–1041. MR**508447**, DOI 10.1090/S0002-9904-1978-14532-7 - H. Niederreiter and Walter Philipp,
*Berry-Esseen bounds and a theorem of Erdős and Turán on uniform distribution $\textrm {mod}\ 1$*, Duke Math. J.**40**(1973), 633–649. MR**337873**, DOI 10.1215/S0012-7094-73-04055-6 - L. Kuipers and H. Niederreiter,
*Uniform distribution of sequences*, Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1974. MR**0419394** - Loo Keng Hua and Yuan Wang,
*Applications of number theory to numerical analysis*, Springer-Verlag, Berlin-New York; Kexue Chubanshe (Science Press), Beijing, 1981. Translated from the Chinese. MR**617192**, DOI 10.1007/978-3-642-67829-5 - H. Niederreiter,
*On a measure of denseness for sequences*, Topics in classical number theory, Vol. I, II (Budapest, 1981) Colloq. Math. Soc. János Bolyai, vol. 34, North-Holland, Amsterdam, 1984, pp. 1163–1208. MR**781180** - H. Niederreiter,
*Quantitative versions of a result of Hecke in the theory of uniform distribution $\textrm {mod}\ 1$*, Acta Arith.**28**(1975/76), no. 3, 321–339. MR**389778**, DOI 10.4064/aa-28-3-321-339

## Additional Information

- © Copyright 1990 American Mathematical Society
- Journal: Math. Comp.
**55**(1990), 289-297 - MSC: Primary 65C10; Secondary 11K45
- DOI: https://doi.org/10.1090/S0025-5718-1990-1023765-9
- MathSciNet review: 1023765