Random numbers for large-scale distributed Monte Carlo simulations

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 75, Issue 6, 2007, Pages

  Bauke, Heiko ^a,b   Mertens, Stephan ^a  

^a OTTO VON GUERICKE UNIVERSITY   (Germany)

^b UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; PARALLEL ALGORITHMS; STATISTICAL MECHANICS; SYSTEMS SCIENCE;

FINITE FIELDS; MULTIPLE LINEAR RECURRENCES; PSEUDORANDOM NUMBERS;

RANDOM NUMBER GENERATION;

EID: 34547357347     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.75.066701     Document Type: Article

References (57)

1. B. Hayes, Am. Sci. AMSCAC 0003-0996 89, 300 (2001).
2. P. D. Coddington, NHSE Review (1996), http://nhse.cs.rice.edu/NHSEreview/ RNG/
3. S. L. Anderson, SIAM Rev. SIREAD 0036-1445 10.1137/1032044 32, 221 (1990).
4. G. Marsaglia, Proc. Natl. Acad. Sci. U.S.A. PNASA6 0027-8424 61, 25 (1968).
5. D. E. Knuth, The Art of Computer Programming, 3rd ed. (Addison Wesley Professional, Reading, MA, 1998), Vol. 2.
6. P. L'Ecuyer, in Handbook of Computational Statistics, edited by, J. E. Gentle, W. Härdle, and, Y. Mori, (Springer, New York, 2004).
7. D. H. Lehmer, Proceedings of the 2nd Symposium on Large-Scale Digital Calculating Machinery, Cambridge, MA (Harvard University Press, Cambridge, MA, 1951), pp. 141-146.
8. D. E. Knuth, The Art of Computer Programming, 1st ed. (Addison Wesley Professional, Reading, MA, 1969), Vol. 2.
9. S. Tezuka, Uniform Random Numbers: Theory and Practice (Kluwer Academic, Boston, 1995).
10. P. L'Ecuyer, F. Blouin, and R. Couture, ACM Trans. Model. Comput. Simul. ATMCEZ 1049-3301 3, 87 (1993).
11. D. Jungnickel, Finite Fields: Structure and Arithmetics (Bibliographisches Institut, Mannheim, 1993).
12. J. Massey, IEEE Trans. Inf. Theory IETTAW 0018-9448 10.1109/TIT.1969. 1054260 15, 122 (1969).
13. A. J. Menezes, Handbook of Applied Cryptography, The CRC Press Series on Discrete Mathematics and its Applications (CRC, Boca Raton, FL, 1996).
14. M. Matsumoto and T. Nishimura, ACM Trans. Model. Comput. Simul. ATMCEZ 1049-3301 10.1145/272991.272995 8, 3 (1998).
15. S. W. Golomb, Shift Register Sequences, revised ed. (Aegan Park, Laguna Hills, CA, 1982).
16. R. Lidl and H. Niederreiter, Introduction to Finite Fields and their Applications, 2nd ed. (Cambridge University Press, Cambridge, England, 1994).
17. R. Lidl and H. Niederreiter, Encyclopedia of Mathematics and its Applications, 2nd ed. (Cambridge University Press, Cambridge, England, 1997), Vol. 20.
18. J. Fillmore and M. Marx, SIAM Rev. SIREAD 0036-1445 10.1137/1010059 10, 342 (1968).
19. N. Zierler, J. Soc. Ind. Appl. Math. JSIMAV 0368-4245 7, 31 (1959).
20. Z.-X. Wan, Lectures on Finite Fields and Galois Rings (World Scientific, Singapore, 2003).
21. A. Compagner, Am. J. Phys. AJPIAS 0002-9505 10.1119/1.16747 59, 700 (1991).
22. A. Compagner, J. Stat. Phys. JSTPBS 0022-4715 10.1007/BF01029989 63, 883 (1991).
23. O. E. Percus and M. H. Kalos, J. Parallel Distrib. Comput. JPDCER 0743-7315 6, 477 (1989).
24. M. Mascagni, Parallel Comput. ZZZZZZ 0167-8191 24, 923 (1998).
25. A. D. Matteis and S. Pagnutti, Parallel Comput. ZZZZZZ 0167-8191 13, 193 (1990).
26. A. D. Matteis and S. Pagnutti, Parallel Comput. ZZZZZZ 0167-8191 14, 207 (1990).
27. J. Eichenauer-Herrmann and H. Grothe, Numer. Math. NUMMA7 0029-599X 10.1007/BF01396346 56, 609 (1989).
28. P. L'Ecuyer, Commun. ACM CACMA2 0001-0782 10.1145/84537.84555 33, 85 (1990).
29. S. Kirkpatrick and E. P. Stoll, J. Comput. Phys. JCTPAH 0021-9991 10.1016/0021-9991(81)90227-8 40, 517 (1981).
30. R. M. Ziff, Comput. Phys. CPHYE2 0894-1866 12, 385 (1998).
31. P. Grassberger, Phys. Lett. A PYLAAG 0375-9601 10.1016/0375-9601(93) 91122-L 181, 43 (1993).
32. L. N. Shchur, J. R. Heringa, and H. W. J. Blöte, Physica A PHYADX 0378-4371 10.1016/S0378-4371(97)00126-X 241, 579 (1997).
33. A. M. Ferrenberg, D. P. Landau, and Y. J. Wong, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.69.3382 69, 3382 (1992).
34. H. Bauke and S. Mertens, J. Stat. Phys. JSTPBS 0022-4715 10.1023/B:JOSS.0000012521.67853.9a 114, 1149 (2004).
35. S. Mertens and H. Bauke, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.69.055702 69, 055702 (R) (2004).
36. P. L'Ecuyer, Oper. Res. OPREAI 0030-364X 47, 159 (1999).
37. A. Grube, Z. Angew. Math. Mech. ZAMMAX 0044-2267 53, T223 (1973).
38. P. L'Ecuyer, ACM Trans. Model. Comput. Simul. ATMCEZ 1049-3301 3, 87 (1993).
39. P. L'Ecuyer, Proceedings of the 2001 Winter Simulation Conference (IEEE Press, Washington, DC, 2001), pp. 95-105.
40. P. L'Ecuyer and P. Hellekalek, Random and Quasi-Random Point Sets, Lecture Notes in Statistics Vol. 138 (Springer, New York, 1998), pp. 223-266.
41. L. Schrage, ACM Trans. Math. Softw. ACMSCU 0098-3500 10.1145/355826. 355828 5, 132 (1979).
42. W. H. Payne, J. R. Rabung, and T. P. Bogyo, Commun. ACM CACMA2 0001-0782 12, 85 (1969).
43. M. Mascagni and H. Chi, Parallel Comput. ZZZZZZ 0167-8191 30, 1217 (2004).
44. Tina's Random Number Generator Library, http://tina.nat.uni-magdeburg.de/ trng/
45. GNU Scientific Library, http://www.gnu.org/software/gsl/
46. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge University Press, Cambridge, England, 1992).
47. M. Lüscher, Comput. Phys. Commun. CPHCBZ 0010-4655 10.1016/0010-4655(94)90232-1 79, 100 (1994).
48. W. E. Brown, M. Fischler, J. Kowalkowski, and M. Paterno, Random Number Generation in C++0X: A Comprehensive Proposal, version 2 (2006);
49. http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2006/n2032.pdf
50. U. Wolff, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.62.361 62, 361 (1989).
51. A. E. Ferdinand and M. E. Fisher, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.185.832 185, 832 (1969).
52. D. Wang and A. Compagner, Math. Comput. MCMPAF 0025-5718 60, 363 (1993).
53. M. Matsumoto and Y. Kurita, ACM Trans. Model. Comput. Simul. ATMCEZ 1049-3301 6, 99 (1996).
54. I. Vattulainen, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.59.7200 59, 7200 (1999).
55. G. Marsaglia, in Computer Science and Statistics: Proceedings of the 16th Symposium on the Interface, Atlanta, Georgia, 1984, edited by, L. Billard, (North Holland, Amsterdam, 1985).
56. Z.-X. Wan, Lectures on Finite Fields and Galois Rings (World Scientific, Singapore, 2003).
57. P. L'Ecuyer, Oper. Res. OPREAI 0030-364X 47, 159 (1999).