Abstract
Calculation of the multidimensional cubatures in unit hypercube is a complex problem of numerical methods, and its application value is great. This paper compares various calculation methods: product of regular one-dimensional grid formulae, classical Monte Carlo method using pseudorandom points and the Sobol sequences. It is suggested to use not any Sobol sequences, but only the ones with magic numbers N equal to powers of 2. In addition, the shifted Sobol points are proposed: all coordinates of the magic Sobol points are simultaneously increased by 1/(2N). Comparisons on the test showed that the latter method is significantly more accurate than all the others.
Published Version
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