Invariants of optimal integration of rapidly oscillatory functions: Fìz.-mat. model. ìnf. tehnol. 2021, 32:121-125 - Zadiraka, Valeriy; Luts, Liliya; Shvidchenko, Inna (PHYSICO-MATHEMATICAL MODELLING AND INFORMATIONAL TECHNOLOGIES, 2021)
The paper presents some common elements (invariants) of optimal integration of rapidly oscillatory functions for the different types of oscillations, in particular, for calculating the Fourier transform from finite functions, wavelet transform, and Bessel transform. Their brief description is given. The application of the invariants allows to increase the potential of quadrature formulas due to the fullest use of apriori information. Invariants form the basis of computer technology of integration of rapidly oscillatory functions with a given accuracy with limited computational resources. References Sergienko, I. V., Lytvyn, O. M. (2018).New information operators in mathematical modeling. K.: Naukova dumka. (in Ukrainian). Zadiraka, V. K. (1983). The theory of computing the Fourier transform. K.: Naukova dumka. (in Russian) Zadiraka, V. K., Luts, L. V., Shvidchenko, I. V. (2020). Optimal numerical integration. Cybernetics and Computer Technologies, 4, 47–64. (in Ukrainian) DOI doi.org/10.34229/2707-451x.20.4.4 Zadiraka, V. K., Melnikova, S. S., Luts, L. V. (2010). Optimal quadrature formulas for computation of continuous wavelet transforms of functions in certain classes. Journal of Automation and Information Sciences, 42(5), 30–44. DOI doi.org/10.1615/jautomatinfscien.v42.i5.40 Zadiraka, V. K., Luts, L. V. (2021). Optimal for accuracy quadrature formulas for calculating of the Bessel transformation for certain classes of sub-integral functions. Cybernetics and Systems Analysis, 57(2), 81–95. (in Ukrainian) DOI doi.org/10.1007/s10559-021-00349-7 Bakhvalov, N. S. (1973). Numerical methods. M.: Nauka. (in Russian) Zadiraka, V. K., Melnikova, S. S., Luts, L. V. (2013). Optimal integration of rapidly oscillating functions in the class W 2,L,N with the use of different information operators. Cybernetics and Systems Analysis, 49, 229–238. DOI doi.org/10.1007/s10559-013-9504-5 Luts, L. V. (2008). Estimation of quality of some quadrature formulas of calculation of integrals of fast-oscillating functions. Shtuchnyj Intelekt, 4, 671–682. (in Ukrainian) http://dspace.nbuv.gov.ua/handle/123456789/7665 Khimich, A. N, Molchanov, I. N., Popov, A. V., Chistyakova, T. V., Yakovlev, M. F. (2008). Parallel algorithms for solving problems of computational mathematics. K.: Naukova dumka. (in Russian)