EFFICIENT COMPUTATION OF SOBOL’ QUASI-RANDOM GENERATOR

Main Article Content

Timotej Vesel

Keywords

algorithm, time complexity, quasi-random generator, Sobol’ sequence, quasi-Monte Carlo simulation

Abstract

Purpose of the study: The quasi-Monte Carlo method is an important tool for modelling and analysing various complex problems in engineering, physical sciences, finance and business. The crucial element of the method is a sequence of deterministic quasi-random values, which is often obtained by using the Sobol’ quasi-random generator. The purpose of this study is to consider the time complexity of generating the Sobol’ sequence.


Methodology: Algorithms for determining the Sobol’ sequence have been studied. The algorithms have been implemented in the Python programming language.


Main Findings: It is established that this sequence can be generated in the linear time provided that generated numbers are based on 32-bit or 64-bit integers. The main result of the paper is the algorithm which enables this time-bound.


Applications of this study: The study can be applied in engineering, physical sciences, finance and business.


Novelty/Originality of this study: It is shown that Sobol’ sequence can be generated in linear time.    

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