Geodesic
Parallel algorithm for pseudorandom numbers generation
Matematičeskoe modelirovanie, Tome 21 (2009) no. 6, pp. 59-68.

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An algorithm for pseudorandom numbers generation on parallel machines, providing concordant formation of segments of random numbers sequence on each processor, is considered. 
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M. V. Iakobovski. Parallel algorithm for pseudorandom numbers generation. Matematičeskoe modelirovanie, Tome 21 (2009) no. 6, pp. 59-68. http://geodesic.mathdoc.fr/item/MM_2009_21_6_a4/

[1] S. S. Lapushkin, M. Kh. Brenerman, M. V. Yakobovskii, “Modelirovanie dinamicheskikh protsessov filtratsii v perkolyatsionnykh reshetkakh na vysokoproizvoditelnykh vychislitelnykh sistemakh”, Matematicheskoe modelirovanie, 16:11 (2004), 77–88 | MR | Zbl

[2] P. L'Ecuyer, F. Panneton, $\mathbb F_2$-Linear Random Number Generators, GERAD Report 2007-21, 2007; to appear with minor revisions in Advancing the Frontiers of Simulation: A Festschrift in Honor of George S. Fishman

[3] H. Haramoto, M. Matsumoto, T. Nishimura, F. Panneton, P. L'Ecuyer, Efficient Jump Ahead for $\mathbb F_2$-Linear Random Number Generators, GERAD Report G-2006-62. Revised May 2007, 2006; INFORMS Journal on Computing (to appear)

[4] P. L'Ecuyer, “Uniform Random Number Generation”, chapter 3, Elsevier Handbooks in Operations Research and Management Science: Simulation, eds. S. G. Henderson, B. L. Nelson, Elsevier Science, Amsterdam, 2006, 55–81

[5] N. A. Konovalov, V. A. Kryukov, “DVM-podkhod k razrabotke parallelnykh programm dlya vychislitelnykh klasterov i setei”, Otkrytye sistemy, 2002, no. 3

[6] V. A. Kryukov, R. V. Udovichenko, “Otladka DVM-programm”, Programmirovanie, 2001, no. 3, 19–29

[7] N. A. Konovalov, V. A. Kryukov, A. A. Pogrebtsov, Yu. L. Sazanov, “S-DVM yazyk razrabotki mobilnykh parallelnykh programm”, Programmirovanie, 1999, no. 1, 54–65 | Zbl

[8] Yu. Yu. Tarasevich, Perkolyatsiya: teoriya, prilozheniya, algoritmy, Uchebnoe posobie, Editorial URSS, M., 2002, 112 pp.

[9] Richard P. Brent, “Uniform Random Number Generators for Supercomputers, Computer Sciences Laboratory, Australian National University”, Proceedings Fifth Australian Supercomputer Conference, 5ASC Organising Committee (Melbourne, December 1992), 1992, 95–104

[10] Knut Donald Ervin, Iskusstvo programmirovaniya. Tom 2. Poluchislennye algoritmy, Uch pos., 3-e izdanie, Per s angl., Izdatelskii dom “Vilyams”, M., 2001, 832 pp.

[11] G. Marsaglia, “Random numbers fall mainly on the planes”, Proc. Nat. Acad. Sci. USA, 61:1 (1968), 25–28 | DOI | MR | Zbl

[12] I. M. Sobol, Chislennye metody Monte-Karlo, Nauka, M., 1973 | MR

[13] P. Khorovits, U. Khill, Iskusstvo skhemotekhniki, V 2-kh tomakh, T. 2, Per. s angl., Mir, M., 1983, 590 pp.

[14] F. Panneton, P. L'Ecuyer, “On the Xorshift Random Number Generators”, ACM Transactions on Modeling and Computer Simulation, 15:4 (2005), 346–361 | DOI

[15] R. P. Brent, On the Periods of Generalized Fibonacci Recurrences, Technical Report TRCS-92-03, Computer Sciences Laboratory, ANU, March 1992

[16] L. Yu. Barash, “Algoritm AKS proverki chisel na prostotu i poisk konstant generatorov psevdosluchainykh chisel”, Bezopasnost informatsionnykh tekhnologii, 2 (2005), 27–38

[17] V. Zhelnikov, Kriptografiya ot papirusa do kompyutera, ABF, M., 1996, il., 336 s.

[18] John Brillhart, D. H. Lehmer, J. L. Selfridge, Bryant Tuckerman, S. S. Wagstaff (Jr.), Factorizations of $b^n+1$, $b=2,3,5,6,7,10,11,12$, up to High Powers, Third Edition, American Mathematical Society, 2002, 236 pp. | MR

[19] G. Marsaglia, The Marsaglia random number CDROM including the DIEHARD battery of tests of randomness, , 1996 http://stat.fsu.edu/pub/

[20] M. V. Yakobovskii, Biblioteka generatsii psevdosluchainykh chisel lrnd32, Distributiv , 2007 http://www.imamod.ru/projects/FondProgramm/RndLib/lrnd32_v02

[21] M. V. Yakobovskii, Svidetelstvo ob ofitsialnoi registratsii v Federalnoi sluzhbe po intellektualnoi sobstvennosti, patentam i tovarnym znakam programmy dlya EVM “Programma soglasovannogo formirovaniya posledovatelnostei psevdosluchainykh chisel na mnogoprotsessornykh vychislitelnykh sistemakh lrnd32”, No 2007613876 ot 12.09.2007

[22] C. D. Lorenz, R. M. Ziff, “Precise determination of the bond percolation thresholds and finite-size scaling corrections for the sc, fcc, and bcc lattices”, Phys. Rev. E, 57 (1998), 230–236 | DOI

[23] H. Kesten, “The critical probability of bond percolation on the square lattice equals 1/2”, Comm. Math. Phys., 74 (1980), 41–59 | DOI | MR | Zbl