IMPACT OF INTEGRAL DIMENSIONS ON HALTON AND SOBOL SEQUENCES PERFORMANCE
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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