On the optimal Halton sequence

Mathematics and Computers in Simulation

Volumn 70, Issue 1, 2005, Pages 9-21

  Chi, H ^a,d   Mascagni, M ^b   Warnock, T ^c  

^a FLORIDA A AND M UNIVERSITY   (United States)

^b Florida State University   (United States)

^c LOS ALAMOS NATIONAL LABORATORY   (United States)

^d FLORIDA STATE UNIVERSITY   (United States)

Author keywords

Correlation; Optimal Halton sequence; Quasi Monte Carlo; Scrambling

Indexed keywords

ALGORITHMS; COMPUTER SIMULATION; CONVERGENCE OF NUMERICAL METHODS; CORRELATION METHODS; FUNCTIONS; INVERSE PROBLEMS; RANDOM NUMBER GENERATION;

CORRELATIONS; OPTIMAL HALTON SEQUENCE; QUASI-MONTE CARLO; SCRAMBLING;

MONTE CARLO METHODS;

EID: 23744447718     PISSN: 03784754     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.matcom.2005.03.004     Document Type: Article

References (24)

1. E. Braaten, and G. Weller An improved low-discrepancy sequence for multidimensional quasi-Monte Carlo integration J. Comput. Phys. 33 1979 249 258
2. E. Brunner, and A. Uhl Optimal multipliers for linear congruential pseudo-random number generators with prime moduli: parallel computation and properties BIT 68 1999 249 260
3. G. Casella Statistical Inference 1990 Brooks/Cole Pub. Co Pacific Grove, CA
4. P.J. Davis, and P. Rabinowitz Methods of Numerical Integration 1984 Academic Press New York
5. B. Fox Implementation and relative efficiency of quasirandom sequence generators ACM Trans. Math. Software 12 1986 362 376
6. J. Halton On the efficiency of certain quasirandom sequences of points in evaluating multidimensional integrals Numerische Mathematik. 2 1960 84 90
7. L. Kocis, and W. Whiten Computational investigations of low discrepancy sequences ACM Trans. Math. Software 23 1997 266 294
8. R. Lidl, and H. Niederreiter Introduction to Finite Fields and Their Applications 1994 Cambridge University Press Cambridge
9. M. Mascagni, and H. Chi On the scrambled Halton sequences Monte Carlo Meth. Appl. 10 2004 435 442
10. M. Mascagni, and H. Chi Optimal quasi-Monte Carlo valuation of derivative securities M. Costantino C. Brebbia Computational Finance and its Applications 2004 WIT Press Southampton, Boston 177 185
11. J. Matousek On the L 2 -discrepancy for anchored boxes J. Complex. 14 1998 527 556
12. W.J. Morokoff, and R.E. Caflish Quasirandom sequences and their discrepancy SIAM J. Sci. Comput. 15 1994 1251 1279
13. H. Niederreiter Quasi-Monte Carlo methods and pseudorandom numbers Bull. Am. Math. Soc. 84 1978 957 1041
14. H. Niederreiter Random Number Generation and Quasi-Monte Carlo Methods 1992 SIAM Philadephia
15. A.B. Owen. Randomly permuted (t, m, s ) -nets and (t, s ) -sequences. Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, 106 in Lecture Notes in Statistics, 1995, pp. 299-317.
16. S.H. Paskov, and J.F. Traub Faster valuation of financial derivatives J. Portfolio Manage. 22 1 1995 113 120
17. J. Spanier, and E.H. Maize Quasi-random methods for estimating integrals using relatively small samples SIAM Rev. 36 1 1994 18 44
18. S. Tezuka Uniform Random Numbers, Theory and Practice 1995 Kluwer Academic Publishers New York
19. B. Tuffin. Improvement of Halton sequences distribution. Technical Report No. 998. IRISA, Resses, 1996.
20. X. Wang, and K.T. Fang The effective dimension and quasi-Monte Carlo J. Complex. 19 2 2003 101 124
21. X. Wang, and F.J. Hickernell Randomized Halton sequences Math. Comput. Model. 32 2000 887 899
22. T. Warnock Computational investigations of low discrepancy point sets S.K. Zaremba Applications of Number Theory to Numerical Analysis 1972 Academic Press New York 319 343
23. T. Warnock Computational investigations of low discrepancy point sets II H. Niederreiter Monte Carlo and Quasi-Monate Carlo Methods in Scientific Computing 1995 Springer 354 361
24. T. Warnock. Effective error estimates for quasi-Monte Carlo computations. Uncertainty Quantification Working Group and Related Special Seminars, http://www.public.lanl.gov/kmh/uncertainty/meetings/warnvgr.pdf, 2002.