The exponent of discrepancy is at most 1.4778...

Mathematics of Computation

Volumn 66, Issue 219, 1997, Pages 1125-1132

  Wasilkowski, Grzegorz W ^a   Woźniakowski, Henryk ^b,c  

^a UNIVERSITY OF KENTUCKY   (United States)

^b Department of Earth and Environmental Sciences   (United States)

^c UNIVERSITY OF WARSAW   (Poland)

Author keywords

Average case; Discrepancy; Multivariate integration

Indexed keywords

EID: 0040151239     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0025-5718-97-00824-7     Document Type: Article

References (16)

1. J. Beck and W. W. L. Chen, Irregularities of distribution, Cambridge University Press, Cambridge, 1987. MR 88m:11061
2. V. A. Bykovskij. On exact order of optimal quadrature formulas for spaces of functions with bounded mixed derivatives, Report of the Dalnevostochnoi Center of Academy of Sciences, Vladivostok, USSR (in Russian), 1985.
3. B. Chazelle, Geometric discrepancy revisited, 34th Annual Symposium on Foundations of Computer Science, 1993, pp. 392-399. CMP 95:11
4. D. P. Dobkin and D. P. Mitchell, Random-edge discrepancy of supersampling patterns, Graphics Interface '93, York, Ontario, 1993.
5. p, 2 ≤ p ≤ ∞, Dokl. Akad. Nauk SSSR 252 (1980), 805-807. MR 81k:10087
6. 2 discrepancy, Math. Comp. 65 (1996), 1621-1633. CMP 96:01
7. S. Heinrich and A. Keller, Quasi-Monte Carlo methods in computer graphics, Part I: The QMC-buffer, Report, Univ. of Kaiserslautern, Dept. Computer Science, Report No.242/1994; Part II: The radiance equation, Report, Univ. of Kaiserslautern, Dept. Computer Science, Report No.243/1994.
8. S. Heinrich and A. Keller, Quasi-Monte Carlo methods in computer graphics, Part I: The QMC-buffer, Report, Univ. of Kaiserslautern, Dept. Computer Science, Report No.242/1994; Part II: The radiance equation, Report, Univ. of Kaiserslautern, Dept. Computer Science, Report No.243/1994.
9. H. Niederreiter, Quasi-Monte Carlo methods and pseudo-random, numbers, Bull. Amer. Math. Soc. 84 (1978), 957-1041. MR. 80d:65016
10. _, Random number generation and quasi-Monte Carlo methods, CBMS-NSF Reg. Conf. Series Appl. Math., vol. 63, SIAM, Philadelphia, 1992. MR 93h:65008
11. K. F. Roth, On irregularities of distribution, Mathematika 1 (1954), 73-79. MR 16:575c
12. _, On irregularities of distribution, IV, Acta Arith. 37 (1980), 67-75. MR 82f:10063
13. I. H. Sloan and S. Joe, Lattice methods for multiple integration, Oxford Science Publication, Oxford, 1994.
14. V. N. Temlyakov, Approximation of functions with bounded mixed derivatives. Proc. Steklov Inst. Math., Moscow, 1989. MR 90e:00007
15. G. W. Wasilkowski and H. Woźniakowski, Explicit cost bounds of algorithms for multivariate tensor product problems, J. Complexity 11 (1995), 1-56. MR 95k:65138
16. H. Woźniakowski, Average case complexity of multivariate integration, Bull. Arner. Math. Soc. (N.S.) 24 (1991), 185-194. MR 91i:65224