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An optimal Monte Carlo method for numerical integration of multidimensional integrals is proposed and studied. It is know that the best possible order of the mean square error of a Monte Carlo integration method over the class of the k times differentiate functions of d variables is Ο (Ν~*~?}. In this paper we present two algorithms implementing the method under consideration. Estimates for the computational complexity are obtained. Numerical tests showing the efficiency of the algorithms are also given.

A new optimal Monte Carlo method for calculating integrals of smooth functions