IMPACT OF INTEGRAL DIMENSIONS ON HALTON AND SOBOL SEQUENCES PERFORMANCE

  • NADIA AKRAM MOHAMMED; Dept. of Mathematics, College of Basic Education, University of Duhok, Kurdistan Region-Iraq
  • SHAFIKA SULTAN ABDULLAH Dept. of Highways and Bridges Engineering, College of Technical Engineering, Duhok Polytechnic University, Kurdistan Region-Iraq
Keywords: Monte Carlo:, Quasi-Monte Carlo:, Halton sequence:, Sobol sequence:

Abstract

Halton and Sobol sequences are two of the most popular number sets used in quasi-Monte Carlo methods.  These sequences are effectively used instead of pseudo random numbers in the evaluation of integrals. In this paper, the two sequences are compared in terms of the size of the number sets and dimensionality. The comparison is implemented with Matlab programming for evaluating numerical integrals. The absolute error values of the investigated integral tests, with constant number of points (n) show that the optimum performance of Sobol is better than Halton at dimension 2 of test 1 and at dimension 2 of test 2. Performance of sequences have been analysed with different dimensions and (n)s. The practical results show that, except for the first dimension, Sobol sequence is better than Halton sequence with output values more stable and low-discrepancy feature  when the dimension value is increased while this feature is deteriorated with Halton sequence.

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Published
2019-10-29
How to Cite
AKRAM MOHAMMED;, N., & SULTAN ABDULLAH, S. (2019). IMPACT OF INTEGRAL DIMENSIONS ON HALTON AND SOBOL SEQUENCES PERFORMANCE. Journal of Duhok University, 22(1), 17-25. https://doi.org/10.26682/sjuod.2019.22.1.3
Section
Pure and Engineering Sciences