Skip to main content

Advertisement

Springer Nature Link
Log in

On the error of the interpolation by bilinear splines

  • Published:
Ukrainian Mathematical Journal Aims and scope

    We’re sorry, something doesn't seem to be working properly.

    Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract

We study the problem of approximation of functions from the classes Wr,s H ω and Wr,s H ω,2by bilinear splines. For some values ofr ands, we obtain exact estimates of the error.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Yu. S. Zav'yalov, V. I. Kvasov, and V. L. Miroshnichenko,Methods of Spline Functions [in Russian], Nauka, Moscow (1980).

    Google Scholar 

  2. N. P. Korneichuk,Splines in the Theory of Approximation [in Russian], Nauka, Moscow (1984).

    Google Scholar 

  3. V. F. Storchai, “Approximation of continuous functions of two variables by spline functions in the metric ofC,” in:Studies in Contemporary Problems of Summation and Approximation of Functions and Their Applications [in Russian], Dnepropetrovsk (1972), pp. 82–89.

  4. V. F. Storchai, “Approximation of functions of two variables by polyhedral functions in a uniform metric,”Izv. Vyssh. Uchebn. Zaved. Mat., No. 8, 84–88 (1973).

    Google Scholar 

  5. S. B. Vakarchuk, “On interpolation by bilinear splines,”Mat. Zametki,47, No. 5, 26–29 (1990).

    Google Scholar 

  6. V. N. Malozemov, “Deviation of broken lines,”Vestn. Leningr. Univ., Mat., Mekh., Astr., No. 7, 150–153 (1966).

    Google Scholar 

  7. V. N. Malozemov, “Polygonal interpolation,”Mat. Zametki,1, No. 5, 537–540 (1967).

    Google Scholar 

  8. Sh. E. Mikeladze,Numerical Methods in Mathematical Analysis [in Russian], Gostekhizdat, Moscow (1953).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Tadzhik University, Dushanbe

    M. Sh. Shabozov

Authors
  1. M. Sh. Shabozov
    View author publications

    You can also search for this author inPubMed Google Scholar

Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 11, pp. 1554–1560, November, 1994.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shabozov, M.S. On the error of the interpolation by bilinear splines. Ukr Math J 46, 1719–1726 (1994). https://doi.org/10.1007/BF01058889

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01058889

Keywords