Chebyshev Approximation by Exponential Expression with Relative Error

Cybernetics and Systems Analysis volume 51, pages286–290(2015)Cite this article

Abstract

The properties of the Chebyshev approximation by an exponential expression with the smallest relative error are investigated and the sufficient condition for its existence is established. A method to determine the parameters of such approximation is proposed and justified. The error of the Chebyshev approximation by an exponential expression is estimated. A numerical example confirming the theoretical results is presented.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

US$ 39.95

Tax calculation will be finalised during checkout.

References

  1. 1.

    V. F. Mitin, V. V. Kholevchuk, and B. P. Kolodych, “Ge-on-GaAs film resistance thermometers: Low-temperature conduction and magnetoresistance,” Cryogenics, 51, No. 1, 68–73 (2011).

    Article  Google Scholar 

  2. 2.

    L. V. Ibragimova, “Constants of the velocity of chemical reactions in high-temperature gas CO2,” Matematich. Modelirovanie, 12, No. 4, 3–19 (2000).

    Google Scholar 

  3. 3.

    P. Malachivskyy, “Chebyshev approximation by the sum of a polynomial and a function with one nonlinear parameter,” in: Physical–Mathematical Modeling and Information Technologies [in Ukrainian], Issue 1 (2005), pp. 134–145.

  4. 4.

    B. A. Popov and G. S. Tesler, Approximation of Functions for Engineering Applications [in Russian], Naukova Dumka, Kyiv (1980).

    Google Scholar 

  5. 5.

    B. A. Popov, Uniform Approximation by Splines [in Russian], Naukova Dumka, Kyiv (1989).

    Google Scholar 

  6. 6.

    B. O. Popov and K. V. Sushchik, “Uniform approximation by splines with elements in the form of the sum of a polynomial and a power,” Visn. Lviv. Univ., Ser. Prykl. Matem. ta Inform., No. 1, 196–199 (1999).

  7. 7.

    Ya. V. Pizyur, “Approximation of functions by Hermite splines with exponential elements,” Visn. Nats. Univ. “Lvivska Politekhnika,” No. 566, 68–75 (2006).

Download references

Author information

Affiliations

  1. Ya. S. Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, National Academy of Sciences of Ukraine, Lviv, Ukraine

    P. S. Malachivskyy & N. V. Danchak

  2. National University “Lviv Polytechnic,”, Lviv, Ukraine

    Ya. V. Pizyur

  3. Ukrainian Academy of Printing, Lviv, Ukraine

    E. B. Orazov

Authors
  1. P. S. Malachivskyy
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ya. V. Pizyur
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. N. V. Danchak
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. E. B. Orazov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to P. S. Malachivskyy.

Additional information

Translated from Kibernetika i Sistemnyi Analiz, No. 2, March–April, 2015, pp. 145–150.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Malachivskyy, P.S., Pizyur, Y.V., Danchak, N.V. et al. Chebyshev Approximation by Exponential Expression with Relative Error. Cybern Syst Anal 51, 286–290 (2015). https://doi.org/10.1007/s10559-015-9720-2

Download citation

Keywords

  • Chebyshev (uniform) approximation
  • points of alternation
  • relative error
  • kernel of approximation error