Quasi-Monte Carlo Node Sets from Linear Congruential Generators
نویسندگان
چکیده
In this paper we present a new approach to nding good lattice points. We employ the spectral test, a well-known gure of merit for uniform random number generators. This concept leads to an assessment of lattice points g that is closely related to the classical Babenko-Zaremba quantity (g; N). The associated lattice rules are good uniformly over a whole range of dimensions. Our numerical examples suggest that this simple approach leads to quasi-Monte Carlo node sets that perform very well in comparison to the best available (t; m; s)-nets.
منابع مشابه
On the Linear Complexity Profile of Nonlinear Congruential Pseudorandom Number Generators with Dickson Polynomials
Linear complexity and linear complexity profile are important characteristics of a sequence for applications in cryptography and MonteCarlo methods. The nonlinear congruential method is an attractive alternative to the classical linear congruential method for pseudorandom number generation. Recently, a weak lower bound on the linear complexity profile of a general nonlinear congruential pseudor...
متن کاملAn Efficient Randomized Quasi-Monte Carlo Algorithm for the Pareto Distribution
This paper studies a new randomized quasi-Monte Carlo method for estimating the mean and variance of the Pareto distribution. In many Monte Carlo simulations, there are some stability problems for estimating the population Pareto variance by using the sample variance. In this paper, we propose a randomized quasi-random number generator [quasiRNG] to generate Pareto random samples, such that the...
متن کاملThe Monte Carlo Algorithm with a Pseudorandom Generator
We analyze the Monte Carlo algorithm for the approximation of multivariate integrals when a pseudorandom generator is used. We establish lower and upper bounds on the error of such algorithms. We prove that as long as a pseudorandom generator is capable of producing only finitely many points, the Monte Carlo algorithm with such a pseudorandom generator fails for ¿2 or continuous functions. It a...
متن کاملStatement of Contribution Close-point Spatial Tests and Their Application to Random Number Generators Close-point Spatial Tests and Their Application to Random Number Generators
Statement Ideally, a random number generator used for a given simulation problem should pass statistical tests closely related to that problem. But tailoring special tests for each problem is impractical. General purpose generators must then be submitted to a wide range of varied statistical tests, sensitive to diierent types of defects in the generator. In this article, we study statistical te...
متن کاملPseudo-random number generators for Monte Carlo simulations on ATI Graphics Processing Units
Basic uniform pseudo-random number generators are implemented on ATI Graphics Processing Units (GPU). The performance results of the realized generators (multiplicative linear congruential (GGL), XOR-shift (XOR128), RANECU, RANMAR, RANLUX and Mersenne Twister (MT19937)) on CPU and GPU are discussed. The obtained speed-up factor is hundreds of times in comparison with CPU. RANLUX generator is fo...
متن کامل