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Analysis of the Results of a Computing Experiment to Restore the Discontinuous Functions of Two Variables Using Projections. II

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Cybernetics and Systems Analysis Aims and scope

Abstract

This article continues a series of publications under the same name. It performs further improvement of the method for recovering discontinuous functions of two variables using projections in order to improve the accuracy of approximation without the Gibbs phenomenon. To this end, it is proposed to construct a discontinuous spline so that the difference between the function being approximated and this spline is a differentiable function. This function is restored using finite Fourier sums whose Fourier coefficients are found using projections. A method for calculating these coefficients is proposed. In the computing experiment, it was assumed that the approximated function has discontinuities of the first kind on a given system of circles or ellipses nested into each other. Analysis of the calculation results confirmed the theoretical statement of the study. The method makes it possible to obtain a prescribed approximation accuracy with a smaller number of projections, i.e., with less irradiation.

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References

  1. O. M. Lytvyn and O. G. Lytvyn, “Analysis of the results of a computing experiment to restore the discontinuous functions of two variables using projections,” Cybern. Syst. Analysis, Vol. 57, No. 5, 754–763 (2021). https://doi.org/10.1007/s10559-021-00400-7.

  2. O. M. Lytvyn, O. G. Lytvyn, O. O. Lytvyn, and V. I. Mezhuyev, “The method of reconstructing discontinuous functions using projections data and finite Fourier sums,” in: 9th Intern. Sci. and Pract. Conf. “Information Control Systems & Technologies (ICST-2020)” (Odessa, Ukraine, September 24–26, 2020), Odessa (2020), pp. 661–673.

  3. O. M. Lytvyn and O. G. Lytvyn, “On an approach to the approximation of discontinuous functions using projections and finite Fourier sums,” in: Computational Methods and Information Transformation Systems: A Collection of Papers V Sci. and Techn. Conf. (Lviv, Ukraine, October 4–5, 2018), Karpenko Physico-Mechanical Institute of the NAS of Ukraine, Lviv, (2018), pp. 8–11.

  4. O. M. Lytvyn, “Periodic splines and a new method to solve the flat problem of X-ray computed tomography,” Bulletin of the Kharkiv State Polytechnic University, Ser. Systems Analysis, Control, and Information Technology, Issue 125, KhDPU, Kharkiv (2000), pp. 27–35.

  5. I. V. Sergienko, V. K. Zadiraka, O. M. Lytvyn, and I. I. Pershyna, Theory of Discontinuous Splines and Its Application in Computed Tomography [in Ukrainian], Naukova Dumka, Kyiv (2017).

  6. O. M. Lytvyn, Interlineation of Functions and Some of Its Applications [in Ukrainian], Osnova, Kharkiv (2002).

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Authors and Affiliations

  1. Ukrainian Engineering Pedagogics Academy, Kharkiv, Ukraine

    O. M. Lytvyn

  2. Kharkiv National University of Radio Electronics, Kharkiv, Ukraine

    O. G. Lytvyn

Authors
  1. O. M. Lytvyn
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  2. O. G. Lytvyn
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Correspondence to O. M. Lytvyn.

Additional information

Continued from No. 5, 2021.

Translated from Kibernetyka ta Systemnyi Analiz, No. 1, January–February, 2022, pp. 110–121.

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Lytvyn, O.M., Lytvyn, O.G. Analysis of the Results of a Computing Experiment to Restore the Discontinuous Functions of Two Variables Using Projections. II. Cybern Syst Anal 58, 95–106 (2022). https://doi.org/10.1007/s10559-022-00439-0

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  • DOI: https://doi.org/10.1007/s10559-022-00439-0

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