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Abstract: this memory size, one should expect a period length close to m , but the actual period length cannot exceed m \Gamma 1. A big waste! Observe that (17) is a special case of (15), with A i = a i I. An interesting idea is to "twist" the recurrence (17) slightly so that each a i I is replaced by a matrix A i such that the corresponding recurrence (15) has full period length m \Gamma 1 while its implementation remains essentially as fast as (17). Matsumoto and Kurita [95, 96] proposed a... (Update)
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BibTeX entry: (Update)
@misc{ l'ecuyer-random,
author = "Pierre L'Ecuyer",
title = "Random Number Generation",
url = "citeseer.ist.psu.edu/630842.html" }
Citations (may not include all citations):2003 The Art of Computer Programming (context) - Knuth - 1981
335 Statistics for Spatial Data (context) - Cressie - 1993
309 Random Number Generation and Quasi-Monte Carlo Methods (context) - Niederreiter - 1992
291 Simulation Modeling and Analysis (context) - Law, Kelton - 1991
175 Stochastic Simulation (context) - Ripley - 1987
159 A Guide to Simulation (context) - Bratley, Fox et al. - 1987
103 A simple unpredictable pseudo-random number generator (context) - Blum, Blum et al. - 1986
87 Random number generators: Good ones are hard to find (context) - Park, Miller - 1988
60 The Mathematica Book (context) - Wolfram - 1996
57 A current view of random number generators (context) - Marsaglia - 1985
57 Improved methods for calculating vectors of short length in .. (context) - Fincke, Pohst - 1985
52 Monte Carlo: Concepts (context) - Fishman - 1996
49 Random number generators on vector supercomputers and other .. (context) - Anderson - 1990
43 A new class of random number generators (context) - Marsaglia, Zaman - 1991
39 Uniform Random Numbers: Theory and Practice (context) - Tezuka - 1995
38 A review of pseudorandom number generators (context) - James - 1990
35 An exhaustive analysis of multiplicative congruential random.. (context) - Fishman - 1986
35 Random numbers generated by linear recurrence modulo two (context) - Tausworthe - 1965
26 A more portable fortran random number generator (context) - Schrage - 1979
25 Inversive and linear congruential pseudorandom number genera.. (context) - Leeb, Wegenkittl - 1997
23 Efficient and secure pseudo-random number generation (context) - Vazirani, Vazirani - 1984
23 Mathematical methods in large scale computing units (context) - Lehmer - 1951
22 A nonlinear congruential pseudorandom number generator with .. (context) - Eichenauer, Lehn et al. - 1988
22 A nonlinear congruential pseudorandom number generator (context) - Eichenauer, Lehn - 1986
21 Mersenne twister: A 623-dimensionally equidistributed unifor.. (context) - Matsumoto, Nishimura - 1998
20 Fourier analysis of uniform random number generators (context) - Coveyou, MacPherson - 1967
19 Random number generators for MIMD parallel processors (context) - Percus, Kalos - 1989
19 Monte Carlo simulations: Hidden errors from (context) - Ferrenberg, Landau et al. - 1992
18 the lattice structure of certain linear congruential sequenc.. (context) - Couture, L'Ecuyer - 1994
17 Distribution Theory for Tests Based on the Sample Distributi.. (context) - Durbin - 1973
17 How to calculate shortest vectors in a lattice (context) - Dieter - 1975
16 Structural properties for two classes of combined random num.. (context) - L'Ecuyer, Tezuka - 1991
15 Generalized feedback shift register pseudorandom number algo.. (context) - Lewis, Payne - 1973
15 Latin supercube sampling for very high dimensional simulatio.. - Owen - 1998
14 dimensional vectors for simple and combined Tausworthe seque.. (context) - Couture, L'Ecuyer et al. - 1993
13 Thoughts on pseudorandom number generators (context) - Ripley - 1990
13 Design of practical and provably good random number generato.. (context) - Aiello, Rajagopalan et al. - 1996
13 An efficient and portable pseudo-random number generator (context) - Wichmann, Hill - 1986
13 Efficient and portable combined Tausworthe random number gen.. (context) - Tezuka, L'Ecuyer - 1991
13 New developments in uniform pseudorandom number and vector g.. (context) - Niederreiter - 1995
11 Inversive pseudorandom number generators: Concepts - Hellekalek - 1995
10 Bad subsequences of well-known linear congruential pseudoran.. (context) - Entacher - 1998
10 Using linear congruential generators for parallel random num.. (context) - Durst - 1989
10 Maximally equidistributed combined Tausworthe generators (context) - L'Ecuyer - 1996
10 A portable high-quality random number generator for lattice .. (context) - Luscher - 1994
10 Operational conditions for random number generation (context) - Compagner - 1995
10 Twisted GFSR generators II (context) - Matsumoto, Kurita - 1994
9 Uniform random number generation (context) - L'Ecuyer - 1994
9 A search for good multiple recursive random number generator.. (context) - L'Ecuyer, Blouin et al. - 1993
9 Parallelization of random number generators and long-range c.. (context) - De Matteis, Pagnutti - 1988
9 Good parameters and implementations for combined multiple re.. (context) - L'Ecuyer - 1997
9 Distribution properties of multiply-with-carry random number.. - Couture, L'Ecuyer - 1997
9 Efficient and portable combined random number generators (context) - L'Ecuyer - 1989
8 RANLUX: A Fortran implementation of the high-quality pseudor.. (context) - James - 1994
8 An asymptotically random Tausworthe sequence (context) - Tootill, Robinson - 1973
8 the use of reducible polynomials as random number generators (context) - Wang, Compagner - 1993
8 Tests for the uniform distribution (context) - Stephens - 1986
8 A class of parallel random number generators (context) - De Matteis, Pagnutti - 1990
8 The Handbook of Random Number Generation and Testing with TE.. (context) - Dudewicz, Ralley - 1981
8 The hierarchy of correlations in random binary sequences (context) - Compagner - 1991
8 Probabilistic algorithms for primality testing (context) - Rabin - 1980
8 DIEHARD: a battery of tests of randomness (context) - Marsaglia - 1996
7 Yet another rng (context) - Marsaglia - 1994
7 distribution of generalized feedback shift register pseudora.. (context) - Fushimi, Tezuka - 1983
7 An equivalence relation between Tausworthe and GFSR sequence.. (context) - Fushimi - 1989
6 Pseudorandom numbers (context) - Lagarias - 1993
6 An implementation of the lattice and spectral tests for mult.. (context) - L'Ecuyer, Couture - 1997
6 unpredictable (context) - L'Ecuyer, Proulx - 1989
6 Parallel pseudorandom number generation using additive lagge.. - Mascagni, Robinson et al. - 1995
6 A random number generator based on the combination of four L.. (context) - L'Ecuyer, Andres - 1997
6 Modern Cryptology - A Tutorial (context) - Brassard - 1988
6 Tests based on EDF statistics (context) - Stephens - 1986
6 Tables of maximally equidistributed combined LFSR generators (context) - L'Ecuyer - 1998
5 the add-with-carry and subtract-with-borrow random number ge.. (context) - Tezuka, L'Ecuyer et al. - 1994
5 Twisted GFSR generators (context) - Matsumoto, Kurita - 1992
5 Tests of pseudo-random numbers (context) - Atkinson - 1980
4 The multiple-recursive matrix method for pseudorandom number.. (context) - Niederreiter - 1995
4 Portable random number generators (context) - Press, Teukolsky - 1992
3 Probability and the Weighting of Evidence (context) - Good - 1950
3 On combining pseudorandom number generators (context) - Brown, Solomon - 1979
3 Implementation of a distributed pseudorandom number generato.. (context) - Chen, Whitlock - 1995
3 Entropy tests for random number generators - L'Ecuyer, Compagner et al. - 1997
3 A limit on the usable length of a pseudorandom sequence (context) - MacLaren - 1992
3 A portable random number generator well suited for the rejec.. (context) - Hormann, Derflinger - 1993
3 Increasing the orders of equidistribution of the leading bit.. (context) - Fushimi - 1983
3 A multiple recursive nonlinear congruential pseudorandom num.. (context) - Eichenauer, Grothe et al. - 1987
3 A pseudorandom vector generator based on finite field arithm.. (context) - Niederreiter - 1986
3 Compound random number generators (context) - Collings - 1987
3 Random numbers for simulation (context) - L'Ecuyer - 1990
3 Testing random number generators (context) - L'Ecuyer - 1992
3 Coding the Lehmer pseudorandom number generator (context) - Payne, Rabung et al. - 1969
3 Implementing a portable FORTRAN uniform (context) - Marse, Roberts - 1983
3 Matrix generators for pseudo-random vectors generation (context) - Grothe - 1987
3 Linear recurrences with carry as random number generators (context) - Couture, L'Ecuyer - 1995
3 Inversive congruential pseudorandom numbers: A tutorial (context) - Eichenauer-Herrmann - 1992
2 the structure of quadratic congruential sequences (context) - Eichenauer, Lehn - 1987
2 Sparse serial tests of randomness (context) - L'Ecuyer, Simard et al. - 1998
2 A pseudo-random number generator for the system/360 (context) - Lewis, Goodman - 1969
2 Computation of a shortest vector and Minkowski-reduced bases.. (context) - Couture, L'Ecuyer - 1996
2 La g'en'eration pseudo-al'eatoire cryptographiquement s'ecur.. (context) - Boucher - 1994
2 Numerical Computations Guide - Microsystems - 1991
2 The serial test for pseudorandom numbers generated by the li.. (context) - Niederreiter - 1985
2 Close-point spatial tests and their application to random nu.. (context) - L'Ecuyer, Cordeau et al. - 1997
2 Implementing a random number package with splitting faciliti.. (context) - L'Ecuyer, Cot'e - 1991
2 Pseudorandom number generation by nonlinear methods (context) - Eichenauer-Herrmann - 1995
2 A new inversive congruential pseudorandom number generator w.. (context) - Eichenauer-Herrmann, Grothe - 1992
1 the period length of generalized inversive pseudorandom numb.. (context) - Huber - 1994
1 Recurring-with-carry sequences (context) - Koc - 1995
1 The Marsaglia random number CDROM (context) - Marsaglia - 1996
1 A remark on algorithm AS 98: The spectral test for the evalu.. (context) - Hoaglin, King - 1978
1 Strong deviations from randomness in m63 sequences based on .. (context) - Matsumoto, Kurita - 1996
1 Uniform random number generators for parallel computers (context) - De'ak - 1990
1 Combined multiple recursive random number generators (context) - L'Ecuyer - 1996
1 How random are random numbers (context) - Good - 1969
1 Bad lattice structures for vectors of non-successive values .. (context) - L'Ecuyer - 1997
1 A history of distribution sampling prior to the era of compu.. (context) - Teichroew - 1965
1 Tests based on sum-functions of spacings for uniform random .. (context) - L'Ecuyer - 1997
1 Pseudorandom vector generation by the multiple-recursive mat.. (context) - Niederreiter - 1995
1 pseudo-random number generator (context) - Moreau - 1996
1 Statistical independence of a new class of inversive congrue.. (context) - Eichenauer-Herrmann - 1993
1 On generalized inversive congruential pseudoran58 dom number.. (context) - Eichenauer-Herrmann - 1994
1 TestU01: Un logiciel pour appliquer des tests statistiques `.. (context) - L'Ecuyer - 2000
1 Random number generators (context) - Hull - 1962
1 the period length of pseudorandom vector sequences generated.. (context) - Eichenauer-Herrmann, Grothe et al. - 1989
1 An improved upper bound for the discrepancy of quadratic con.. (context) - Eichenauer-Herrmann, Niederreiter - 1995
Documents on the same site (http://www.iro.umontreal.ca/~lecuyer/papers.html): More
Lattice Rules for the Simulation of Ruin Problems - Lemieux, L'Ecuyer (Correct)
Lattice Computations for Random Numbers - Couture, L'Ecuyer (1999) (Correct)
Maximally Equidistributed Combined Tausworthe Generators - L'Ecuyer (1996) (Correct)
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