New Cubature Formulas for Sobolev Spaces with Dominant Mixed Derivative

Bassarov S. Nursultanov E.
June 2025 Springer

Journal of Mathematical Sciences (United States)
2025 #291 Issue 1 4 - 19 pp.

We present new cubature formulas for multivariate periodic functions with respect to each variable with period 1 and some smoothness α > max(1/q, 1/2), where 1 ≤ q ≤ ∞. The new cubature formulas are exact for polynomials with frequencies from the corresponding hyperbolic cross, and the upper bound of the worst-case error is ON-αlogNα+1/q~n-1 for periodic functions in the Sobolev spaces Wqα, where N is the number of nodes, q~=minq,2, n is the dimension. The feature of our methods is that the error is represented in terms of Fourier coefficients.

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Gumilyov Eurasian National University, 2, Satbaev St, Astana, 010000, Kazakhstan
Kazakhstan Branch of Lomonosov Moscow State University, 11, Kazhymukan Munaitpasov St., Astana, 020000, Kazakhstan

Gumilyov Eurasian National University
Kazakhstan Branch of Lomonosov Moscow State University

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