Random Numbers. Sequences Based On Linear Feedback


Diploma Thesis, 2012

128 Pages, Grade: 2


Abstract or Introduction

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 pseudo-random 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 FSR-based 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.

Details

Title
Random Numbers. Sequences Based On Linear Feedback
College
Klagenfurt University  (Institut für Statistik)
Grade
2
Author
Year
2012
Pages
128
Catalog Number
V302951
ISBN (eBook)
9783668014565
ISBN (Book)
9783668014572
File size
5321 KB
Language
English
Keywords
random, numbers, random numbers, sequence, pattern, algorithm, pseudo-random numbers, equidistribution, period, feedback shift register, polynomial, characteristic polynomial, primitive, primitive polynomial, sparse polynomials, deficiency, modify feedback, filter, filter output, combine generators
Quote paper
Christian Mößlacher (Author), 2012, Random Numbers. Sequences Based On Linear Feedback, Munich, GRIN Verlag, https://www.grin.com/document/302951

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