- Clearly, C can be identi ed as a set of bi-in nite words con- tained in R. In this paper, we analyze the language complexity of C w.r.t. Ω ω several well-known properties, namely number-conservation, surjectivity, injec- tivity, sensitivity to initial conditions and equicontinuity.
- Tapla, and J. Thompson, 'A random number generator for continuous random variables based on an Interpolation procedure of Aklma,' Proceedings of the 1978 Winter Simulation Conference, pp. 228-230, 1078.
- Nonuniform random variate generation is concerned with the generation of random variables with certain distributions. Such random variables are often discrete, taking values in a countable set, or absolutely continuous, and thus described by a density.
- Source code with cost as a nonuniform random number generator Article (PDF Available) in IEEE Transactions on Information Theory 46(2):712 - 717 April 2000 with 31 Reads DOI: 10.1149.
- The Complexity Of Nonuniform Random Number Generation Pdf Reader Download
- The Complexity Of Nonuniform Random Number Generation Pdf Reader Online
- The Complexity Of Nonuniform Random Number Generation Pdf Reader Free
The complexity of nonuniform random number generation. In Algorithms and Complexity: New Directions and Recent Results, Academic Press.
The Complexity Of Nonuniform Random Number Generation Pdf Reader Download
- Ahrens JH, Dieter U (1974) Computer methods for sampling from gamma, beta, Poisson and binomial distributions. Computing 12:223–246MathSciNetzbMATHCrossRefGoogle Scholar
- Altman NS (1988) Bitwise behavior of random number generators. SIAM J Sci Stat Comput 9:941–949MathSciNetzbMATHCrossRefGoogle Scholar
- Anderson TW, Darling DA (1952) Asymptotic theory of certain “goodness-of-fit” criteria based on stochastic processes. Ann Math Stat 23:193–212MathSciNetzbMATHCrossRefGoogle Scholar
- Applegate D, Kannan R (1991) Sampling and integration of near log-concave functions. In: Proceedings of the ACM symposium on theory of computingGoogle Scholar
- Bárány I, Füredi Z (1987) Computing the volume is difficult. Discrete Comput Geom 2:319–326MathSciNetzbMATHCrossRefGoogle Scholar
- Bellare M, Goldwasser S, Micciancio D (1997) “Pseudo-random” number generation within cryptographic algorithms: the DSS case. Springer, New YorkGoogle Scholar
- Bertsimas D, Vempala S (2004) Solving convex programs by random walks. J ACM 51:540–556MathSciNetzbMATHCrossRefGoogle Scholar
- Blum L, Blum M, Shub M (1986) A simple unpredictable pseudo-random number generator. SIAM J Comput 15:364–383MathSciNetzbMATHCrossRefGoogle Scholar
- Blum L, Cucker F, Shub M, Smale S (1997) Complexity and real computation. Springer, New YorkzbMATHCrossRefGoogle Scholar
- Bollobás B (1997) Volume estimates and rapid mixing. In: Levy S (ed) Flavors of geometry. Cambridge University Press, Cambridge, pp 151–194Google Scholar
- Couture R, L’Ecuyer P (1998) Special issue on uniform random number generation—editorial. ACM Trans Model Comput Simul 8:1–2CrossRefGoogle Scholar
- Dabbene F, Shcherbakov PS, Polyak BT (2010) A randomized cutting plane method with probabilistic geometric convergence. SIAM J Optim 20:3185–3207MathSciNetzbMATHCrossRefGoogle Scholar
- Devroye LP (1986) Non-uniform random variate generation. Springer, New YorkzbMATHGoogle Scholar
- Devroye LP (1997) Random variate generation for multivariate unimodal densities. ACM Trans Model Comput Simul 7:447–477zbMATHCrossRefGoogle Scholar
- Diaconis P, Hanlon P (1992) Eigen-analysis for some examples of the Metropolis algorithm. Contemp Math 138:99–117MathSciNetCrossRefGoogle Scholar
- Dyer ME, Frieze AM, Kannan R (1991) A random polynomial-time algorithm for approximating the volume of convex bodies. J ACM 38:1–17MathSciNetzbMATHCrossRefGoogle Scholar
- Frieze A, Hastad J, Kannan R, Lagarias JC, Shamir A (1988) Reconstructing truncated linear variables satisfying linear congruences. SIAM J Comput 17:262–280MathSciNetzbMATHCrossRefGoogle Scholar
- Gentle JE (1998) Random number generation and Monte Carlo methods. Springer, New YorkzbMATHGoogle Scholar
- Hastings WK (1970) Monte Carlo sampling methods using Markov Chains and their applications. Biometrika 57:97–109zbMATHCrossRefGoogle Scholar
- Hellekalek P (1998) Good random number generators are (not so) easy to find. Math Comput Simul 46:487–507MathSciNetCrossRefGoogle Scholar
- Hellekalek P, Larcher G (eds) (1998) Random and quasi-random point sets. Springer, New YorkzbMATHGoogle Scholar
- Jerrum M, Sinclair A (1996) The Markov Chain Monte Carlo method: an approach to approximate counting and integration. In: Hochbaum DS (ed) Approximation algorithms for NP-hard problems. PWS Publishing, Boston, pp 482–520Google Scholar
- Kalai AT, Vempala S (2006) Simulated annealing for convex optimization. Math Oper Res 31(2):253–266MathSciNetzbMATHCrossRefGoogle Scholar
- Kannan R, Lovász L, Simonovits M (1997) Random walks and an O∗(n5) volume algorithm for convex bodies. Random Struct Algorithms 11:1–50zbMATH3.0.CO%3B2-X'>CrossRefGoogle Scholar
- Khachiyan LG (1989) The problem of computing the volume of polytopes is NP-hard. Usp Mat Nauk 44:179–180 (in Russian)MathSciNetzbMATHGoogle Scholar
- Knuth DE (1998) The art of computer programming. Seminumerical algorithms, vol 2. Addison-Wesley, ReadingGoogle Scholar
- Lecchini-Visintini A, Lygeros A, Maciejowski J (2010) Stochastic optimization on continuous domains with finite-time guarantees by Markov chain Monte Carlo methods. IEEE Trans Autom Control 55:2858–2863MathSciNetCrossRefGoogle Scholar
- L’Ecuyer P (1994) Uniform random number generation. Ann Oper Res 53:77–120MathSciNetzbMATHCrossRefGoogle Scholar
- L’Ecuyer P, Blouin F, Couture R (1993) A search for good multiple recursive random number generators. ACM Trans Model Comput Simul 3:87–98zbMATHCrossRefGoogle Scholar
- Lehmer DH (1951) Mathematical methods in large-scale computing units. In: Proceedings of the second symposium on large-scale digital calculation machineryGoogle Scholar
- Lovász L (1996) Random walks on graphs: a survey. In: Sós VT, Miklós D, Szönyi T (eds) Combinatorics, Paul Erdös is eighty. János Bolyai Mathematical Society, Budapest, pp 353–398Google Scholar
- Lovász L (1999) Hit-and-run mixes fast. Math Program 86:443–461MathSciNetzbMATHCrossRefGoogle Scholar
- Matsumoto M, Nishimura T (1998) Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator. ACM Trans Model Comput Simul 8:3–30zbMATHCrossRefGoogle Scholar
- Mengersen KL, Tweedie RL (1996) Rates of convergence of the Hastings and Metropolis algorithms. Ann Stat 24:101–121MathSciNetzbMATHCrossRefGoogle Scholar
- Metropolis N, Rosenbluth AW, Rosenbluth MN, Teller A, Teller H (1953) Equations of state calculations by fast computing machines. J Chem Phys 21:1087–1091CrossRefGoogle Scholar
- Meyn SP, Tweedie RL (1996) Markov chains and stochastic stability. Springer, New YorkGoogle Scholar
- Niederreiter H (1995) New developments in uniform pseudorandom number and vector generation. In: Niederreiter H, Shiue PJ-S (eds) Monte Carlo and quasi-Monte Carlo methods in scientific computing. Springer, New York, pp 87–120CrossRefGoogle Scholar
- Papoulis A, Pillai SU (2002) Probability, random variables and stochastic processes. McGraw-Hill, New YorkGoogle Scholar
- Rubinstein RY, Kroese DP (2008) Simulation and the Monte-Carlo method. Wiley, New YorkzbMATHGoogle Scholar
- Smith RL (1984) Efficient Monte-Carlo procedures for generating points uniformly distributed over bounded regions. Oper Res 32:1296–1308MathSciNetzbMATHCrossRefGoogle Scholar
- Snedecor GW, Cochran WG (1989) Statistical methods. Iowa State Press, AmeszbMATHGoogle Scholar
- Spall JC (2003) Estimation via Markov Chain Monte Carlo. IEEE Control Syst Mag 23:34–45CrossRefGoogle Scholar
- Spall JC (2003) Introduction to stochastic search and optimization: estimation, simulation, and control. Wiley, New YorkzbMATHCrossRefGoogle Scholar
- Tausworthe RC (1965) Random numbers generated by linear recurrence modulo two. Math Comput 19:201–209MathSciNetzbMATHCrossRefGoogle Scholar
- von Neumann J (1951) Various techniques used in connection with random digits. US Nat Bur Stand Appl Math Ser 36–38Google Scholar
Random number generatlon has intrigued sclentists for a few decades, and a lot of effort has been spent on the creation of randomness on a deterministic (non-random) machlne, that is, on the design of computer algorithms that are able to produce ‘random’ sequences of integers.
This is a difficult task. Online ip changer. Such algorithms are called generators, and all generators have flaws because all of them construct the n-th number in the sequence in function of the n-1 numbers preceding it, initialized wlth a nonrandom seed. Numerous quantities have been invented over the years that measure just how ‘random’ a sequence is, and most well-known generators have been subjected to rigorous statistical testing. However, for every generator, it is always possible to and a statistical test of a (possibly odd) property to make the generator flunk.
The mathematical tools that are needed to design and analyze these generators are largely number theoretic and combinatorial. These tools differ drastically from those needed when we want to generate sequences of integers with certain non-uniform distributions, given that a perfect uniform random number generator is available. The reader should be aware that we provide him with only half the story (the second half). The assumption that a perfect uniform random number generator is available is now quite unrealistic, but, with time, it should become less so. Having made the assumption, we can build quite a powerful theory of non-uniform random variate generation.
The Complexity Of Nonuniform Random Number Generation Pdf Reader Online
The Complexity Of Nonuniform Random Number Generation Pdf Reader Free
Non-Uniform Random Variate Generation
by Luc Devroye (PDF, Online reading) – 15 chapters