Business Information Management - Closed

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Browsing Business Information Management - Closed by Subject "Linear congruential generators"

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    Distribution of lattice points
    (Springer Wien, 2006) Sezgin, F.
    We discuss the lattice structure of congruential random number generators and examine figures of merit. Distribution properties of lattice measures in various dimensions are demonstrated by using large numerical data. Systematic search methods are introduced to diagnose multiplier areas exhibiting good, bad and worst lattice structures. We present two formulae to express multipliers producing worst and bad laice points. The conventional criterion of normalised lattice rule is also questioned and it is shown that this measure used with a fixed threshold is not suitable for an effective discrimination of lattice structures. Usage of percentiles represents different dimensions in a fair fashion and provides consistency for different figures of merits.
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    A method of systematic search for optimal multipliers in congruential random number generators
    (Springer Netherlands, 2004) Sezgin, F.
    This paper presents a method of systematic search for optimal multipliers for congruential random number generators. The word-size of computers is a limiting factor for development of random numbers. The generators for computers up to 32 bit word-size are already investigated in detail by several authors. Some partial works are also carried out for moduli of 248 and higher sizes. Rapid advances in computer technology introduced recently 64 bit architecture in computers. There are considerable efforts to provide appropriate parameters for 64 and 128 bit moduli. Although combined generators are equivalent to huge modulus linear congruential generators, for computational efficiency, it is still advisable to choose the maximum moduli for the component generators. Due to enormous computational price of present algorithms, there is a great need for guidelines and rules for systematic search techniques. Here we propose a search method which provides 'fertile' areas of multipliers of perfect quality for spectral test in two dimensions. The method may be generalized to higher dimensions. Since figures of merit are extremely variable in dimensions higher than two, it is possible to find similar intervals if the modulus is very large.