Effective by precision algorithms for approximation of functions from the Gelder class by Fourier’s series: Fìz.-mat. model. ìnf. tehnol. 2021, 32:159-164 - Kolomys, Olena (PHYSICO-MATHEMATICAL MODELLING AND INFORMATIONAL TECHNOLOGIES, 2021)
Effective by precision algorithms for approximation of functions from the Gelder class by Fourier’s series, using the Fourier’s coefficients, calculated with high precision, are constructed, and the evaluations of their basic characteristics (precision and speed) are obtained. References Zadiraka, V. K., Babych, M. D., Berezovsky, A. I. (2003).T-efficient algorithms for approximate solution of problems of computational and applied mathematics. Ternopil, Zbruch. Fichtenholtz, G. M. (2001). Course of differential and integral calculus. M.: Fizmatlit. T. 3. Stepanets, A. I. (2005). Methods of Approximation Theory. VSP: Leiden, Boston. Zadiraka, V. K., Melnikova, S. S. (1993). Digital signal processing. Kiev: Scientific Opinion. Sergienko, I. V., Zadiraka, V. K., Lytvyn, O. M., Melnikova, S. S., Nechuyviter, O. P. (2011). Optimal algorithms for calculating integrals from fast-oscillating functions and their application. Vol. 1 Algorithms. Kiev: Scientific Opinion, 2011. 447 p. Vol. 2 Application. Kiev: Scientific Opinion. Bakhvalov, N. S. (1973). Numerical methods. M.: Nauka. Lutz, L. V. (2008). Quality assessment of some quadrature formulas for calculating integrals from fast-oscillating functions. Artificial Intelligence, 4, 671–682.