Quadrature formulae for classes of functions of low smoothness

Erlan Dautbekovich Nursultanov, Nazerke Tulekovna Tleukhanova

2003

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DOI 10.1070/sm2003v194n10abeh000777
Data confidence 70 medium
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Abstract

For Sobolev and Korobov spaces of functions of several variables a quadrature formula with explicitly defined coefficients and nodes is constructed. This formula is precise for trigonometric polynomials with harmonics from the corresponding step hyperbolic cross. The error of the quadrature formula in the classes , is , where is the number of nodes and is a parameter depending on the class.The problem of the approximate calculation of multiple integrals for functions in is considered in the case when this class does not lie in the space of continuous functions, that is, for .