A Comparison of the Results Obtained by Two Types of Low-Discrepancy Sequences in Quasi-Monte Carlo Method

Dimitrievska Ristovska, Vesna (2017) A Comparison of the Results Obtained by Two Types of Low-Discrepancy Sequences in Quasi-Monte Carlo Method. In: PROCEEDINGS of the 14th Conference on Informatics and Information Technology. Faculty of Computer Science and Engineering, Ss. Cyril and Methodius University in Skopje, Macedonia, Skopje, Macedonia, pp. 75-78. ISBN 978-608-4699-07-1

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Abstract

Quasi-Monte Carlo method is a well-known method for numerical integration and solving many numerical problems using low-discrepancy sequences. The main idea in Quasi Monte Carlo method is to approximate the integral of a function f as the average of the function evaluated at a set of points x1,...,xn. In this paper we consider the absolute errors between the exact value of an definite integral and the results obtained with a numerical integration with Quasi-Monte Carlo method using low-discrepancy sequences: Halton and Sobol sequences. In the experimental computations we choose some different functions on the interval [0,1] in one dimensional case, with different number of points in the sequences. Numerical results and graphical figures verify theoretical results: Quasi-Monte Carlo has a bigger rate of convergence than the rate for Monte Carlo method. Almost all our computations show that Sobol sequence produces better results, with smaller absolute errors than Halton sequence in numerical integration for the all chosen type of functions.

Item Type: Book Section
Subjects: International Conference on Informatics and Information Technologies > Applied Mathematics
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Depositing User: Vangel Ajanovski
Date Deposited: 29 Nov 2017 18:32
Last Modified: 29 Nov 2017 18:32
URI: http://eprints.finki.ukim.mk/id/eprint/11378

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