Approximation of Functions of Three Variables by Finite Fourier Sums Using Tomograms

Abstract

This work continues the authors’ research on the problem of approximation of functions of three variables by finite Fourier sums using tomograms. The main attention is paid to the calculation of 3D Fourier coefficients. In this work, the values of the function at individual points of the integration area, as well as the direct and inverse Radon transformation, are not used directly for their calculation. To calculate these coefficients, tomograms are used - images of traces of an approximate function of three variables on given planes. The numerical implementation of the method related to the calculation of 3D Fourier coefficients and the approximation of functions of three variables is given.The results confirming the effectiveness of the method were obtained.