In the paper, some approaches to the numerical integration of multivariate functions are presented. Approaches that are considered include the use of quadrature formulae, solving a system of polynomial equations, and the probabilistic method Monte Carlo. The main part of the paper presents the construction of formulae with positive weights. Boundaries on the number of nodes of such formulae are derived and systems of equations that give us nodes and weights are presented. In the end examples of these formulae are given and their errors are examined.
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