RANDOM NUMBERS SEQUENCES BASED ON LINEAR FEEDBACK

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ISBN: 9783668014572 Géneros: PBT Sinópsis: Diploma Thesis from the year 2012 in the subject Mathematics Stochastics grade 2 Klagenfurt University Institut fur Statistik language English abstract 7 is definately not a random number In fact we would probably say that the sequence 7 2 13 9 5 8 is random Within mathematics a sequence of random numbers should not display a pattern or show any form of regularity Sequences of random numbers are generated by an algorithm that determines a succeeding number using one or more given numbers Numbers yielded by an algorithm are called pseudorandom numbers which can be denoted mathematically Multidimensional equidistribution and a large period are important properties required from a sequence in order to acknowledge it as random numbers The algorithms to produce random numbers can be roughly grouped into two families congruential generators and generators based on feedback shift registers FSR We will focus on the latter family An FSRbased generator can be described by a characteristic polynomial which has to be primitive in order to ensure the best quality with respect to randomness Often sparse polynomials are used to reduce computing costs The algorithms used produce random sequences that might have some deficiencies However the quality of randomness can be improved by several measurements as are modifying the feedback filtering the output sequences or combining two or more generators
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