UDC 519.6
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2 Kharkiv National University of Radio Electronics, Kharkiv, Ukraine
 litvinog@ukr.net
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ANALYSIS OF THE RESULTS OF A COMPUTING EXPERIMENT TO RESTORE
THE DISCONTINUOUS FUNCTIONS OF TWO VARIABLES USING PROJECTIONS. IIІ
Abstract. This article continues the series of publications by the authors under the same name.
It performs further improvement of the method of restoring the discontinuous functions
of two variables using projections in order to increase the accuracy of approximation without
the Gibbs phenomenon for the case where the discontinuity lines are a system of boundaries of squares nested in each other.
Compared with the previous two parts of this study, we consider the case where the discontinuity
lines have angular points at which the derivative of the normal is indefinite. It is proposed to construct
a discontinuous spline so that the difference between the approximate function and this spline
is a continuous or differential function. This function is approximated by finite Fourier sums whose Fourier coefficients
can be found using projections. An analysis of the results of the computational experiment show their compliance with the theoretical statements of the study.
Keywords: computed tomography, discontinuous function, discontinuous spline, class of differentiation, Gibbs phenomenon, Fourier sum.
FULL TEXT
REFERENCES
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- Lytvyn O.M., Lytvyn O.G. Analysis of the results of a computational experiment to restore the discontinuous functions of two variables using projections. ІI. Kibernetyka ta systemnyi analiz. 2021. 2022. Vol. 58, N 1. P. 110–121.
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