COT 5715: Random Number Generation
General Bibliography & Papers for Students to Present in Class

  1. J. H. Ahrens and U. Dieter, Non-Uniform Random Numbers, Institut für Mathematische Statistik, Technische Hochschule, Graz, Austria, 1974.
  2. N. S. Altman, "Bit-wise behavior of random number generators," SIAM J. Sci. Stat. Comput., 9: 941-949,1988.
  3. S. L. Anderson, "Random number generators on vector supercomputers and other advanced architectures," SIAM Review, 32: 221-251, 1990.
  4. S. Aluru and G. M. Prabhu and J. Gustafson, "A random number generator for parallel computers," Parallel Computing, 18: 839-847, 1992.
  5. D. L. Andrè and G. L. Mullen and H. Niederreiter, "Figures of merit for digital multistep pseudorandom number generators," Mathematics of Computation, 54: 737-748, 1990.
  6. A. C. Arvillas and D. G. Maritsas, "Partitioning the period of a class of m-sequences and applications to pseudorandom number generation," J. of the ACM, 25: 675-686, 1978.
  7. B. C. Bromley, "Quasirandom number generator for parallel Monte Carlo algorithms," Journal of Parallel and Distributed Computing, 38: 101-104, 1996.
  8. W. A. Beyer and R. B. Roof and D. Williamson, "The lattice structure of multiplicative pseudo-random vectors," Mathematics of Computation, 25: 345-363, 1971.
  9. G. E. P. Box and M. E. Miller, "A note on the generation of normal random deviates," Ann. Math. Stat., 29: 610-611, 1958
  10. E. Braaten and G. Weller, "An Improved Low-Discrepancy Sequence for Multidimensional Quasi-Monte Carlo Integration," Journal of Computational Physics, 33: 249-258, 1979.
  11. P. Bratley and B. L. Fox, "Algorithm 659: Implementing Sobol's  quasirandom sequence generator," ACM transactions on Mathematical Software, 14(1): 88-100, 1988.
  12. P. Bratley and B. L. Fox and H. Niederreiter, "Implementation and tests of low-discrepancy sequences," ACM Transactions on Modeling and Computer Simulation, 2: 195-213, 1992.
  13. R. P. Brent, "Uniform Random Number Generators for Supercomputers," in "Proceedings of the Fifth Australian Supercomputer Conference", pp. 95-104, 1992.
  14. R. P. Brent, "On the periods of generalized Fibonacci recurrences," Mathematics of Computation, 63: 389-401, 1994.
  15. B.C. Bromley, "Quasirandom number generators for parallel Monte Carlo algorithms," Journal of Parallel and Distributed Computing, 38: 101-104, 1996.
  16. R.E. Caflisch, "Monte Carlo and quasi-Monte Carlo methods," Acta Numerica, 7: 1-49, 1998.
  17. H. Chaix and H. Faure, "Discrepance et diaphonie en dimension un," Acta Arithmetica, 63: 103-141, 1993.
  18. P. Coddington, "Analysis of random number generators using Monte Carlo simulation," Int. J. of Mod. Phys. C, 5: 547-560, 1994.
  19. P. Coddington, "Tests of random number generators using Ising model simulations," Int. J. of Mod. Phys. C, 7: 295-303, 1996
  20. B. J. Collings and G. B. Hembree, "Initializing generalized feedback shift register pseudorandom number generators," J. of the ACM, 33: 706-711, 1986.
  21. R. R. Coveyou, "Random number generation is too important to be left to chance," Studies in Applied Math., 3: 70-111, 1969.
  22. R. R. Coveyou and R. D. MacPherson, "Fourier analysis of uniform random number generators," J. of the ACM, 14: 100-119, 1967.
  23. R. Couture and P. L'Ecuyer, "On the lattice structure of certain linear congruential sequences related to AWC/SWB generators," Math. Comput., 62: 799-808, 1994.
  24. R. Couture and P. L'Ecuyer, "Distributed properties of multiply-with-carry random number generators," Math. Comput., 66: 591-607, 1997.
  25. S. A. Cuccaro and M. Mascagni and D. V. Pryor, "Techniques for testing the quality of parallel pseudorandom number generators," in "Proceedings of the Seventh SIAM Conference on Parallel Processing for Scientific Computing", SIAM: Philadelphia, Pennsylvania, pp. 279-284, 1995.
  26. I. Deák, "Uniform random number generators for parallel computers," Parallel Computing, 15: 155-164, 1990.
  27. L. Y. Deng and K. H. Chan and Y. Yuan, "Random number generators for multiprocessor systems," Int. J. Model. Simul.. 14: 185-191, 1994.
  28. L. Y. Deng and H. Xu, "A system of high-dimensional, efficient, long-cycle and portable uniform random number generators," ACM Transactions on Modeling and Computer Simulation, 13 (4): 299-309, 2003.
  29. M. Deleglise and J. Rivat, "Computing π(x): the Meissel, Lehmer, Lagarias, Miller, Odlyzko method," Math. Comput., 65: 235-245, 1996.
  30. A. De'Matteis and S. Pagnutti, "Parallelization of random number generators and long-range correlations," Numer. Math., 53: 595-608, 1988.
  31. A. De'Matteis and S. Pagnutti, "A class of parallel random number generators," Parallel Computing, 13: 193-198, 1990.
  32. A. De'Matteis and S. Pagnutti, "Long-range correlations in linear and non-linear random number generators," Parallel Computing, 14: 207-210, 1990.
  33. A. De'Matteis and S. Pagnutti, "Controlling correlations in parallel Monte Carlo", Parallel Computing, 21: 73-84, 1995.
  34. E. De Doncker and R. Zanny and M. Ciobanu and Y. Guan, Distributed quasi Monte-Carlo methods in a heterogeneous environment," in Proceedings of the Heterogeneous Computing Workshop 2000, pp. 200-206, 2000.
  35. L. Devroye, Non-uniform Random Variate Generation, Springer-Verlag:  New York, 1986.
  36. M. J. Durst, "Testing parallel random number generators," in Computing Science and Statistics: Proceedings of the XXth Symposium on the Interface, pp. 228-231, 1988.
  37. M. J. Durst, "Using linear congruential generators for parallel random number generation," in Proceedings of the 1989 Winter Simulation Conference: Society for Computer Simulation,,  E. A. MacNair and K. J. Musselman and P. Heidelberger, eds.,  IEEE Press, pp. 462-466, 1989.
  38. W. F. Eddy, "Random number generators for parallel processors," J. Comput. Appl. Math., 31: 63-71, 1990.
  39. J. Eichenauer-Herrmann, "Inversive congruential pseudorandom numbers avoid the planes," Math. Comput., 56: 297-301, 1991.
  40. J. Eichenauer-Herrmann and E. Herrmann and S. Wegenkittl, "A survey of quadratic and inversive congruential pseudorandom numbers," Lecture Notes in Statistics, 127: 66-97, 1998.
  41. J. Eichenauer and H. Groethe and J. Lehn and A. Topuzŏglu, "A multiple recursive non-linear congruential pseudorandom number generator," Manuscripta Math., 58: 315-326, 1987.
  42. J. Eichenauer and H. Groethe and J. Lehn, "Marsaglia's lattice test and non-linear congruential pseudorandom number generators," Metrika, 35: 241-250, 1988.
  43. J. Eichenauer and J. Lehn, "A nonlinear congruential pseudorandom number generator," Statist. Hefte, 37: 315-326, 1986.
  44. J. Eichenauer and J. Lehn and A. Topuzŏglu, "A nonlinear congruential pseudorandom number generator with power of two modulus," Math. Comput., 51: 757-759, 1988.
  45. J. Eichenauer-Herrmann and H. Groethe and H. Niederreiter and A. Topuzŏglu, "On the lattice structure of non-linear generators with modulus 2α," J. Comput. Appl. Math., 31: 81-85, 1990.
  46. J. Eichenauer-Herrmann, and H. Niederreiter, "Digital inversive pseudorandom numbers," ACM Transactions on Modeling and Computer Simulation, 4: 339-349, 1994.
  47. J. Eichenauer-Herrmann, "Pseudorandom generation by nonlinear methods," International Statistical Review, 63: 247-255, 1995.
  48. K. Entacher, "Bad subsequences of well-known linear congruential pseudorandom number generators," ACM Trans. Model. Comput. Simul., 8: 61-70, 1998.
  49. K. Entacher, "Parallel streams of linear random numbes in the spectral test," ACM Trans. Model. Comput. Simul., 9: 31-44, 1999.
  50. H. Faure, "Using permutations to reduce discrepancy," J. Comp. Appl. Math., 31: 97-103, 1990.
  51. H. Faure, "Good Permutations for Extreme Discrepancy", Journal of Number Theory, 42: 47-56, 1992.
  52. H. Faure, "Discrépance de suites associées à un système de numération (en dimension s)," Acta Arith., 41(4): 337-351, 1982, in French.
  53. H. Faure and S. Tezuka, "A New Generation of Digital (0,s)-Sequences," in Fourth International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, 2000, H. Niederreiter, et al., eds.,  Springer, 2001.
  54. A. M. Ferrenberg and D. P. Landau and Y. J. Wong, "Monte Carlo simulations: Hidden errors from `good' random number generators," Phys. Rev. Let., 69: 3382-3384, 1992.
  55. G. S. Fishman, "Multiplicative congruential random number generators with modulus 2β : an exhaustive analysis for  β = 32 and a partial analysis for  β = 48," Math. Comput., 54: 331-344, 1990.
  56. G. S. Fishman and L. S. Moore III, "An exhaustive analysis of multiplicative congruential random number generators with modulus 231-1," SIAM J. Sci. Stat. Comput., 1: 24-45, 1986.
  57. P. Frederickson and R. Hiromoto and T. L. Jordan and B. Smith and T. Warnock, "Pseudo-random trees in Monte Carlo", Parallel Computing, 1: 175-180, 1984.
  58. P. Frederickson and R. Hiromoto and J. Larson, "A parallel Monte Carlo transport algorithm using a pseudo-random tree to guarantee reproducibility," Parallel Computing, 4: 281-290, 1987.
  59. B. L. Fox, "Algorithm 647: Implementation and Relative Efficiency of Quasirandom Sequence Generators," ACM Transactions on Mathematical Software (TOMS), 12(4): 362-376, 1986
  60. M. Fushimi, "Increasing the orders of equidistribution of the leading bits of the Tausworthe sequence," Inform. Proc. Lett., 16: 189-192, 1983.
  61. M. Fushimi, "An equivalence relation between Tausworthe and GFSR sequences and applications," Applied Math. Lett., 2: 135-137, 1989.
  62. M. Fushimi, "Random number generation on parallel processors," in Proceedings of the 1989 Winter Simulation Conference: Society for Computer Simulation, E. A. MacNair and K. J. Musselman and P. Heidelberger, eds., IEEE Press, pp. 459-461, 1989.
  63. M. Fushimi and S. Tezuka, "The k-distribution of generalized feedback shift register pseudorandom numbers," Comm. of the ACM, 26: 516-523, 1983.
  64. S. W. Golomb, Shift Register Sequences, Revised Edition, Aegean Park Press: Laguna Hills, California, 1982.
  65. E. R. Golder and J. G. Settle, "The Box-Muller method for generating pseudo-random normal deviates," Appl. Statist., 25: 12-20, 1972.
  66. P. Grassberger, "On correlations in 'good' random number generators," Phys. Lett. A, 181: 43-46, 1993.
  67. H. Grothe, "Matrix generators for pseudo-random vector generation," Statist. Hefte., 28: 233-238, 1987.
  68. M. Goresky and A. Klapper, " Efficient multiply-with-carry random number generators with maximal period,," ACM Transactions on Modeling and Computer Simulation, 13: 310-321, 2003.
  69. J. H. Halton, "Pseudo-random trees: multiple independent sequence generators for parallel and branching computations," J. Comput. Phys., 84: 1-56, 1989.
  70. J. H. Halton, "Algorithm 247: Radical-inverse quasi-random point sequence," Communications of the ACM, 7(12): 701-702, 1964. 
  71. J. H. Halton, "On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals," Numer. Math., 2: 84-90, 1960.
  72. J. H. Halton, "Sequential Monte Carlo," Proceedings of the Cambridge Philosophical Society, 58: 57-78, 1962.
  73. J. H. Halton, "Sequential Monte Carlo Techniques for the Solution of Linear Systems", Journal of Scientific Computing, 9: 213-257, 1994.
  74. J. M. Hammersley and D. C. Handscomb, Monte Carlo Methods, Chapman and Hall: London, 1964.
  75. S. Heinrich, "Efficient algorithms for computing the L2-discrepancy," Math. Comput., 65(216): 1621-1633, 1996.
  76. P Hellekalek and H. Niederreiter, "The weighted spectral test: Diaphony," ACM Trans. Model. Comput. Simul., 8: 43-60, 1998.
  77. G. W. Hill, "Cyclic properties of pseudo-random sequences of Mersenne prime residues," Comput. J., 22: 80–85, 1979.
  78. E. Hlwaka, "Funktionen von beschränkter Variation in der Theorie der Gleichverteiling," Ann. Mat. Pura Appl., 54: 325-333, 1961.
  79. T. E. Hull and A. R. Dobell, "Random Number Generators," SIAM Review, 4(3): 230-254, 1962. 
  80. B. L. Holian and O. E. Percus and T. T. Warnock and P. A. Whitlock, "Pseudorandom number generators for massively parallel molecular-dynamics simulations," Phys. Rev. E, 50(2, pt. B): 1607-1615, 1994.
  81. K. Kankaala and T. Ala-Nissila and I. Vattulainen, "Bit level correlations in some pseudorandom number generators," Research Institute for Theoretical Physics, University of Helsinki, Preprint series in theoretical physics: HU-TFT-93-41, 1993.
  82. S. Kirkpatrick and E. P. Stoll, "A very fast shift-register sequence random number generator turbulence simulation," J. Comput. Phys., 40: 517-526, 1981.
  83. L. Kocis and W.J. Whiten, "Computational investigations of low-discrepancy sequences," ACM transactions on Mathematical Software, 23(2): 266-294, 1997.
  84. A. E. Koniges and C. E. Leith, "Parallel processing of random number generation for Monte Carlo turbulence simulation," J. Comput. Phys., 81: 230-235, 1989.
  85. D. E. Knuth, The Art of Computer Programming, Vol. 1: Fundamental Algorithms, Third Edition, Addison-Wesley, Reading, Massachusetts, 1997.
  86. D. E. Knuth, The Art of Computer Programming, Vol. 2: Seminumerical Algorithms, Third Edition, Addison-Wesley, Reading, Massachusetts, 1997.
  87. D. E. Knuth, The Art of Computer Programming, Vol. 3: Sorting and Searching, Second Edition, Addison-Wesley, Reading, Massachusetts, 1998.
  88. N. M. Korobov, Exponential Sums and Their Applications, Kluwer Academic Publishers: Dordrecht, The Netherlands, 1992.
  89. R. A. Kronmal and A. V. Peterson Jr., "On the Alias Method for Generating Random Variablesom a Discrete Distribution," The American Statistician, 33: 214-218, 1979.
  90. L. Kuipers and H. Niederreiter, Uniform Distribution of Sequences, John Wiley and Sons: New York, 1974.
  91. J. C. Lagarias, "Pseudorandom number generators in cryptography and number theory," Proceedings and Symposia in Applied Mathematics (Cryptography and Computational Number Theory), 42: 1-37, Carl Pomerance (ed.), 1990.
  92. J. C. Lagarias, "Pseudorandom numbers," Statistical Science, 8: 31-39, 1993.
  93. J. C. Lagarias and V. S. Miller and A. M. Odlyzko, "Computing π(x): The Meissel-Lehmer method," Mathematics of Computation, 55: 537-560, 1985.
  94. D. P. Landau and D. Stauffer, "Test of parallel updating in Ising model simulation," Journal de Physique, 50: 509-512, 1989.
  95. P. L'Ecuyer, "Efficient and portable combined random number generators," Comm. of the ACM, 31: 742-774, 1988.
  96. P. L'Ecuyer, "Random numbers for simulation," Communications of the ACM, 33:85-97, 1990.
  97. P. L'Ecuyer, "Uniform random number generation," Ann. Oper. Res., 53: 77-120, 1994.
  98. P. L'Ecuyer, and R. Couture, "An Implementation of the Lattice and Spectral Tests for Multiple Recursive Linear Random Number Generators," INFORMS Journal on Computing, 9: 57-60, 1997.
  99. P. L'Ecuyer, "Random number generation," in Handbook of Computational Statistics, J. E. Gentle W. Haerdle and Y. Mori, eds., Springer-Verlag: New York, 2004.
  100. P. L'Ecuyer, "Random Number Generation", chapter 3 of Elsevier Handbooks in Operations Research and Management Science: Simulation, S. G. Henderson and B. L. Nelson, eds., Elsevier Science, Amsterdam, pp. 55-81, 2006.
  101. P. L'Ecuyer, "Good parameter sets for combined multiple recursive random number generators," Operation Research, 47: 169-164, 1999.
  102. P. L'Ecuyer and S. Côté, "Implementing a random number package with splitting facilities ," ACM Transactions on Mathematical Software, 17(1): 98-111, 1991.
  103. P. L'Ecuyer and R. Simard, "TestU01: A C Library for Empirical Testing of Random Number Generators," ACM Transactions on Mathematical Software, 33(4): Article 22, 2007.
  104. D. H. Lehmer, "Mathematical methods in large-scale computing units," in Proceedings of the 2nd Symposium on Large-Scale Digital Calculating Machinery, Harvard University Press: Cambridge, Massachusetts, pp. 141-146, 1949.
  105. A. K. Lenstra, H. W. Lenstra and L. Lovasz, "Factoring polynomials with rational coefficients," Math. Ann., 261: 515-534, 1982.
  106. T. G. Lewis and W. H. Payne, "Generalized feedback shift register pseudorandom number algorithms," Journal of the ACM, 20: 456-468, 1973.
  107. J. X. Li and G. L. Mullen, "Parallel computing of a quasi-Monte Carlo algorithm for valuing derivatives," Parallel Computing, 26: 641-653, 2000.
  108. R. Lidl and H. Niederreiter, Introduction to Finite Fields and Their Applications, Cambridge University Press: Cambridge, London, New York, 1986.
  109. R.. Lidl and H. Niederreiter, "Finite Fields," in Encyclopedia of Mathematics and Its Applications, Addison-Wesley: Reading, Massachusetts, 1983.
  110. M. Lüscher, "A portable high-quality random number generator for lattice field theory simulations," Comp. Phys. Comm., 79: 100-110, 1994.
  111. N. M. MacLaren, "The generation of multiple independent sequences of pseudorandom numbers," Applied Statistics, 38: 351-359, 1989.
  112. J. Makino, "Lagged-Fibonacci random number generators on parallel computers," Parallel Computing, 20: 1357-1367, 1994.
  113. G. Marsaglia, "DIEHARD software package," http://stat.fsu.edu/pub/diehard/
  114. G. Marsaglia, "Random numbers fall mainly in the planes," Proc. Nat. Acad. Sci. U.S.A., 62: 25-28, 1968.
  115. G. Marsaglia, "The structure of linear congruential sequences," in Applications of Number Theory to Numerical Analysis, S. K. Zaremba, ed., Academic Press: New York, pp. 249-285, 1972.
  116. G. Marsaglia, "A current view of random number generators," in Computing Science and Statistics: Proceedings of the XVIth Symposium on the Interface, pp. 3-10, 1985.
  117. G. Marsaglia and T. A. Bray, "A convenient method for generating normal variables," SIAM Review, 6: 260-264, 1964.
  118. G. Marsaglia and L.H. Tsay, "Matrices and the structure of random number sequences," Linear Alg. and Applic., 67: 147-156, 1985.
  119. G. Marsaglia and A. Zaman and W. W. Tsang, "Toward a universal random number generator," Statist. Probab. Lett., 9: 35-39, 1990.
  120. G. Marsaglia and A. Zaman, "A new class of random number generators," The Annals of Applied Probability, 1: 462-480, 1991.
  121. O. Martin and A. M. Odlyzko and S. Wolfram, "Algebraic properties of cellular automata," Comm. Math. Phys., 93: 219-258, 1984.
  122. M. Mascagni, "Random Number Generation," in CRC Standard Mathematical Tables and Formulae 31st Edition, D. Zwillinger, editor, Chapman and Hall/CRC, Boca Raton, pp. 644-649, 2003.
  123. M. Mascagni, "Deterministic Monte Carlo Methods and Parallelism," Sourcebook on Parallel Computing, J. Dongarra, I. Foster, F. Fox, W. Gropp, K. Kennedy, L. Torcson, and A. White, editors, Morgan Kaufman Publishers, San Francisco, pp. 249-258, 2003.
  124. M. Mascagni and S. A. Cuccaro and D. V. Pryor and M. L. Robinson, "Recent Developments in Parallel Pseudorandom Number Generation," in Proceedings of the Sixth SIAM Conference on Parallel Processing for Scientific Computing, volume II, D. E. Keyes and M. R. Leuze and L. R. Petzold and D. A. Reed, eds., SIAM: Philadelphia, Pennsylvania, pp. 524-529, 1993.
  125. M. Mascagni and M. L. Robinson and D. V. Pryor and S. A. Cuccaro, "Parallel pseudorandom number generation using additive lagged-Fibonacci recursions," Lecture Notes in Statistics, 106: 263-277, 1995.
  126. M. Mascagni and S. A. Cuccaro and D. V. Pryor and M. L. Robinson, "A fast, high-quality, and reproducible lagged-Fibonacci pseudorandom number generator," J. Comput. Physics, 15: 211-219. 1995.
  127. M. Mascagni, "Parallel linear congruential generators with prime moduli," Parallel Computing, 24: 923-936, 1998.
  128. M. Mascagni, "Some methods of parallel pseudorandom number generation," in Proceedings of the IMA Workshop on Algorithms for Parallel Processing, R. Schreiber, M. Heath and A. Ranade, eds., Springer-Verlag: New York, Berlin, pp. 277-288, 1999.
  129. M. Mascagni, "Parallel Pseudorandom Number Generation," SIAM News, August, pp. 1,8-10, 1999.
  130. M. Mascagni, "Serial and Parallel Random Number Generation," in Quantum Monte Carlo in Physics and Chemistry, NATO ASI Series, Series C: Mathematical and Physical Sciences, Peter Nightingale and Cyrus Umrigar, eds., Kluwer: Dordrecht, pp. 425-446, 1999.
  131. M. Mascagni and J. Ren, "New Development in the Scalable Parallel Random Number Generator (SPRNG) Library," The Institute of Statistical Mathematics Cooperative Research Report, 210: 120-125, 2008.
  132. M. Mascagni and A. Srinivasan, "Parameterizing Parallel Multiplicative Lagged-Fibonacci Generators," Parallel Computing, 30: 899-916, 2004.
  133. M. Mascagni and A. Srinivasan, "Algorithm 806: SPRNG: A Scalable Library for Pseudorandom Number Generation," ACM Transactions on Mathematical Software, 26: 436-461, 2000.
  134. M. Mascagni and H. Chi, "Parallel linear congruential generators with Sophie-Germain moduli," Parallel Computing, 30(11): 1217-1231, 2004.
  135. J. L. Massey, "Shift-register synthesis and BCH decoding," IEEE Trans. Information Theory, 15: 122-127, 1969,
  136. N. Masuda and F. Zimmermann, "PRNGlib: A parallel random number generator library," Swiss Center for Scientific Computing Technical Report: TR-96-08, 1996.
  137. Makoto Matsumoto and Takuji Nishimura, "Dynamic Creation of Pseudorandom Number Generators", 
    Monte Carlo and Quasi-Monte Carlo Methods 1998, Springer, pp 56-69, 2000. 
  138. M. Matsumoto and Y. Kurita, "Twisted GFSR generators," ACM Trans. Model. Comput. Simul., 2: 179-194, 1992.
  139. M. Matsumoto and T. Nishimura, "Mersenne twister: A 623-dimensionally equidistributed uniform pseudo-random number generator," ACM Trans. Model. Comput. Simul., 8: 3-30, 1998.
  140. W. J. Morokoff and R. E. Caflisch, "Quasi-random sequences and their discrepancies," SIAM Journal on Scientific Computing, 15(6): 1251-1279, 1994.
  141. W. J. Morokoff and R. E. Caflisch, "Quasi-Monte Carlo integration," J. Comp. Phys., 122: 218-230, 1995.
  142. H. R. Neave, "On using the Box-Muller transformation with multiplicative congruential pseudo-random number generators," Appl. Statist., 22: 92-97, 1973.
  143. H. Niederreiter, "Quasi-Monte Carlo methods and pseudo-random numbers," Bull. Amer. Math. Soc., 84: 957-1041, 1978.
  144. H. Niederreiter, "The serial test for pseudo-random numbers generated by the linear congruential method," Numer. Math., 46: 51-68, 1985.
  145. H. Niederreiter, "A statistical analysis of generalized feedback shift register pseudorandom number generators," SIAM J. Sci. Stat. Comput., 8: 1035-1051, 1987.
  146. H. Niederreiter, "Point sets and sequences with small discrepancy," Montash. Math., 103: 269-288, 1987.
  147. H. Niederreiter, "The serial test for digital k-step pseudorandom numbers," Math. J. Okayama Univ., 30: 93-119, 1988.
  148. H. Niederreiter, "Remarks on nonlinear congruential pseudorandom numbers," Metrika, 35: 321-328, 1988.
  149. H. Niederreiter, "Statistical independence of nonlinear congruential pseudorandom numbers," Montash. Math., 106: 149-159, 1988.
  150. H. Niederreiter, "Low-discrepancy and low-dispersion sequences," J. Number Theory, 30: 51-70, 1988.
  151. H. Niederreiter, "The serial test for congruential pseudorandom numbers generated by inversion," Math. Comput., 52: 125-144, 1989.
  152. H. Niederreiter, "Pseudorandom numbers generated from shift register sequences", Lecture Notes in Math., 1452: 165-177, 1990.
  153. H. Niederreiter, "Statistical independence properties of pseudorandom vectors produced by matrix generators," J. Comput. and Appl. Math., 31: 139-151, 1990.
  154. H. Niederreiter, "Lower bounds for the discrepancy of inversive congruential pseudorandom numbers", Math. Comput., 55: 277-287, 1990.
  155. H. Niederreiter, "Recent trends in random number and random vector generation," Ann. Oper. Res., 31: 323-36, 1991.
  156. H. Niederreiter, "Random Number Generation and Quasi-Monte Carlo Methods," SIAM: Philadelphia, Pennsylvania, 1992. (Book review)
  157. H.Niederreiter, "Factorization of polynomials and some linear-algebra problems over finite fields", Linear Algebra and Its Appl. 192, 301-328, 1993.
  158. H. Niederreiter, "On a new class of pseudorandom numbers for simulation methods," J. Comput. Appl. Math., 56: 159-167, 1994.
  159. H. Niederreiter and I. E. Shparlinski, "Recent advances in the theory of nonlinear pseudorandom number generators," in: K.T. Fang, F. Hickernell, H. Niederreiter (Eds.), Monte Carlo and Quasi-Monte Carlo Methods 2000, Springer-Verlag, Berlin, pp. 86-102, 2002.
  160. A. B. Owen, "Randomly Permuted (t,m,s)-Nets and (t,s)-Sequences", Lecture Notes in Statistics, 106: 299-317, 1995.
  161. F. Panneton, P. L'Ecuyer, and M. Matsumoto, "Improved Long-Period Generators Based on Linear Recurrences Modulo 2," ACM Transactions on Mathematical Software, 32(1): 1-16, 2006.
  162. A. Papageorgiou and J. F. Traub, "Faster evaluation of  multidimensional integrals," Computers in Physics, 11(6): 574-579, 1997.
  163. S. H. Paskov, "New methodologies for valuing derivatives," in Mathematics of Derivative Securities, Cambridge University Press, S. Pliska and M. Dempster, eds.,  pp. 545-582, 1997.
  164. S. H. Paskov and J. F. Traub, "Faster evaluation of financial derivatives," Journal of Portfolio Management, Fall:113-120, 1995.
  165. W. H. Press and S. A. Teukolsky and W. T. Vetterling and B. P. Flannery", Numerical Recipes in FORTRAN, Second Edition, Cambridge University Press: New York, 1994.
  166. S. K. Park and K. W. Miller, "Random number generators: good ones are hard to find," Comm. of the ACM, 31: 1192-1201, 1988.
  167. O. E. Percus and J. K. Percus, "Long range correlations in linear congruential generators," J. Comput. Phys., 77: 267-269, 1988.
  168. O. E. Percus and M. H. Kalos, "Random number generators for MIMD parallel processors," J. of Par. Distr. Comput., 6: 477-497, 1988.
  169. W. P. Petersen, "Some evaluations of random number generators in real*8 format," Swiss Center for Scientific Somputing Technical Report: TR-96-06, 1996.
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