Effective by precision algorithms for approximation of functions from the Lipschitz class by Fourier’s series
Keywords:
апроксимація функцій; клас Ліпшиця; ряди Фур’є; коефіцієнти ряду Фур'є; похибка апроксимаціїAbstract
Effective by precision algorithm for approximation of functions from the Lipschitz class by Fourier’s series is developed. The error of approximation of the function is obtained, which consists of two parts: the error arising from the use of a finite number of terms of the series, and the error arising from the approximate determination of the Fourier series coefficients using quadrature formulas for calculating integrals of fast oscillating functions that are optimal in order of accuracy on the Lipschitz class.
References
Fikhtengolts, G. M. (2003). Course of differential and integral calculus (8th ed., Vol.3). Fizmatlit Publisher [in Russian]. https://www.at.alleng.org/d/math/math169.htm
Stepanets, A. I. (2005). Methods of Approximation Theory. VSP International Science Publishers.
Zadiraka, V. K., Melnikova, S. S. (1993). Digital signal processing. Naukova Dumka [in Russian].
Sergienko, I. V., Zadiraka, V. K., Lytvyn, O. M., Melnikova, S. S., Nechuiviter, O. P. (2011). Optimal algorithms for calculating integrals of fast-oscillating functions and their application: Vol.1. Algorithms; Vol.2. Applications. Naukova Dumka [in Ukrainian].
Кolomys, O. M., Lutz, L. V., Liudvychenko, V. O. (2011). Approximation of functions of some classes by Fourier’s series. In Proceedings of the International Youth school of mathematics “The issues of calculation optimization (ISCOPT-XXXVII)” (pp. 74–75). V. M. Glushkov Institute of Cybernetics of NAS of Ukraine [in Ukrainian]. http://iscopt.com.ua/index.php/uk/zbirnik-prats
Кolomys, O. M. (2021). Effective by precision algorithms for approximation of functions from the Gelder class by Fourier’s series. Physico-mathematical modelling and informational technologies, 32, 159–164. [in Ukrainian] http://iscopt.com.ua/index.php/uk/zbirnik-prats
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
