Computer Simulation Techniques: The definitive introduction! by Harry Perros PDF

By Harry Perros

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That is, divide the result by m and set xi+1 equal to the remainder of this division. For example, if x0 = 0, a = c = 7, and m = 10 then we can obtain the following sequence of numbers: 7, 6, 9, 0, 7, 6, 9, 0,... The method using the above expression is known as the mixed congruential method. A simpler variation of this method is the multiplicative congruential method. This method utilizes the relation xi+1=axi(mod m). Historically, multiplicative congruential generators came before the mixed congruential generators.

However, using a prime number may not be very fast. Thus, typically m is set to 232 or 264. In this case the maximum period of the additive LFG is (2k-1)x2m-1. The multiplicative LFG is as follows: xn = xn-j * xn-k (mod m) where m is set to 232 or 264 and 0

For example, let us assume that we are generating 10-digit numbers and that the previous value was 5772156649. The square of this value is 33317792380594909291 and the next number is 7923805949. The question here that arises is how such a method can give a sequence of random numbers. Well, it does not, but it appears to be! The mid-square method was relatively slow and statistically unsatisfactory. It was later abandoned in favour of other algorithms. In the following sections, we describe the the congruential method, the Tausworthe generators, the lagged Fibonacci generators, and the Mersenne twister.

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Computer Simulation Techniques: The definitive introduction! by Harry Perros

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