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Good parameters for a class of node sets in quasi-Monte Carlo integration


Authors: Tom Hansen, Gary L. Mullen and Harald Niederreiter
Journal: Math. Comp. 61 (1993), 225-234
MSC: Primary 11K45; Secondary 65D32
DOI: https://doi.org/10.1090/S0025-5718-1993-1182244-1
MathSciNet review: 1182244
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Abstract: For $ 2 \leq s \leq 12$ we determine good parameters in a general construction of node sets for s-dimensional quasi-Monte Carlo integration recently introduced by the third author. Some of the parameters represent optimal choices in this construction and lead to improvements on node sets obtained by earlier techniques.


References [Enhancements On Off] (What's this?)

  • [1] D. A. André, G. L. Mullen, and H. Niederreiter, Figures of merit for digital multistep pseudorandom numbers, Math. Comp. 54 (1990), 737-748. MR 1011436 (91d:65012)
  • [2] P. Bratley, B. L. Fox, and H. Niederreiter, Implementation and tests of low-discrepancy sequences, ACM Trans. Modeling and Computer Simultation 2 (1992), 195-213.
  • [3] L. K. Hua and Y. Wang, Applications of number theory to numerical analysis, Springer, Berlin, 1981. MR 617192 (83g:10034)
  • [4] G. Larcher, Nets obtained from rational functions over finite fields, Acta Arith. 63 (1993), 1-13. MR 1201615 (94c:11067)
  • [5] D. H. Lehmer, Mathematical methods in large-scale computing units, Proc. 2nd Sympos. on Large-Scale Digital Calculating Machinery (Cambridge, MA, 1949), Harvard Univ. Press, Cambridge, MA, 1951, pp. 141-146. MR 0044899 (13:495f)
  • [6] G. L. Mullen and H. Niederreiter, Optimal characteristic polynomials for digital multistep pseudorandom numbers, Computing 39 (1987), 155-163. MR 919665 (88m:65011)
  • [7] G. L. Mullen and G. Whittle, Point sets with uniformity properties and orthogonal hypercubes, Monatsh. Math. 113 (1992), 265-273. MR 1169232 (93h:11086)
  • [8] H. Niederreiter, Quasi-Monte Carlo methods and pseudo-random numbers, Bull. Amer. Math. Soc. 84 (1978), 957-1041. MR 508447 (80d:65016)
  • [9] -, Multidimensional numerical integration using pseudorandom numbers, Math. Programming Study 27 (1986), 17-38. MR 836749 (87m:11075)
  • [10] -, Rational functions with partial quotients of small degree in their continued fraction expansion, Monatsh. Math. 103 (1987), 269-288. MR 897953 (88h:12002)
  • [11] -, Point sets and sequences with small discrepancy, Monatsh. Math. 104 (1987), 273-337. MR 918037 (89c:11120)
  • [12] -, Low-discrepancy and low-dispersion sequences, J. Number Theory 30 (1988), 51-70. MR 960233 (89k:11064)
  • [13] -, Low-discrepancy point sets obtained by digital constructions over finite fields, Czechoslovak Math. J. 42 (1992), 143-166. MR 1152177 (93c:11055)
  • [14] -, Random number generation and quasi-Monte Carlo methods, SIAM, Philadelphia, PA, 1992. MR 1172997 (93h:65008)
  • [15] -, Orthogonal arrays and other combinatorial aspects in the theory of uniform point distributions in unit cubes, Discrete Math. 106/107 (1992), 361-367. MR 1181933 (94f:11070)
  • [16] -, Finite fields, pseudorandom numbers, and quasirandom points, Proc. Internat. Conf. on Finite Fields, Coding Theory, and Advances in Comm. and Comp. (Las Vegas, 1991), Dekker, New York, 1993, pp. 375-394. MR 1199844 (94a:11121)
  • [17] I. M. Sobol', The distribution of points in a cube and the approximate evaluation of integrals, Zh. Vychisl. Mat. i Mat. Fiz. 7 (1967), 784-802. (Russian) MR 0219238 (36:2321)

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1993-1182244-1
Article copyright: © Copyright 1993 American Mathematical Society

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