Comparing Halton and Sobol Sequences in Integral Evaluation

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, which is the absolute difference between the exact and estimated errors, is plotted against dimensions for different functions. The practical results show that, except the first dimension, Sobol sequence is better than Halton sequence. The results also show that Sobol sequence outputs are more stable.

Keywords

• 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
• which is the absolute difference between the exact and estimated errors
• is plotted against dimensions for different functions. The practical results show that
• except the first dimension