Abstract
In this paper, we consider the calculation of integrals of arbitrary multiplicity by the methods of nonuniform grids, Monte Carlo and optimal coefficients.A comparative analysis of these numerical methods for integrating multiple integrals was made.It was established that the method of optimal coefficients had an advantage compared to other methods.It is shown that the use of uneven and parallelepipedal grids is the basis of almost all results obtained in the field of application of theoretic -numerical methods to the problems of approximate analysis.It is established that interpolation of functions of several variables by theoretic-numerical grids allows to receive interpolation formulas, accuracy of which rises with increase of smoothness of functions.The number of variables in this case has no significant effect on the order of the residual member.The use of the functionto Fourier coefficients allows to obtain an interpolation formula from the quadrature formulas, which are constructed with the help of the parallelepipedal grids.This formula is accurate for trigonometric polynomials, the degree of which does not exceed the value of N N s 2 ln .