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On quadrature formulas. (English. Russian original) Zbl 0602.65008
Sov. Math., Dokl. 29, 616-619 (1984); translation from Dokl. Akad. Nauk SSSR 276, 1038-1041 (1984).
There exist two different approaches to the problem of numerical integration. The first is based on the methods of the theory of functions, the second on the methods of probability theory (the Monte- Carlo method). These two approaches, concerned with one and the same problem of determining an approximate value of a definite integral of a concrete function, speak different languages. Assertions concerning the approximate value of some quantity with a certain probability and statements regarding the exactness of a value of the same quantity, made without enlisting the concept of probability, seem incommensurate. In this note these two approaches to the problem of numerical integration are compared in the same terms.

65D32 Numerical quadrature and cubature formulas
65C05 Monte Carlo methods
41A55 Approximate quadratures