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On the error of the interpolation by bilinear splines

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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.

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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 

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Authors and Affiliations

  1. Tadzhik University, Dushanbe

    M. Sh. Shabozov

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

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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

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

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