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Some Problems of Simultaneous Approximation of Functions of Two Variables and Their Derivatives by Interpolation Bilinear Splines

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Abstract

Exact estimates for the errors of approximation of functions of two variables and their derivatives by interpolation bilinear splines are obtained on certain classes.

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REFERENCES

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

    Google Scholar 

  2. B. M. Shumilov, “On local approximation by bilinear splines,” Metody Splain-Funktsii (Vychislit. Sist.), Issue 81, 42–47 (1979).

  3. V. N. Malozemov, “On polygonal interpolation,” Mat. Zametki, 1, No.5, 537–540 (1967).

    Google Scholar 

  4. S. B. Vakarchuk, “On interpolation by bilinear splines,” Mat. Zametki, 47, No.5, 26–30 (1990).

    Google Scholar 

  5. M. Sh. Shabozov, “Exact estimates of simultaneous approximation of functions of two variables and their derivatives by bilinear splines,” Mat. Zametki, 59, No.1, 142–152 (1996).

    Google Scholar 

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

    Google Scholar 

  7. V. F. Storchai, “Approximation of continuous functions of two variables by spline functions in the metric of C,” in: Investigations in Contemporary Problems of Summation and Approximation of Functions and Their Applications [in Russian], Dnepropetrovsk University, Dnepropetrovsk (1972), pp. 66–68.

    Google Scholar 

  8. V. F. Storchai, “Approximation of continuous functions of two variables by polyhedral functions and spline functions in the uniform metric,” in: Investigations in Contemporary Problems of Summation and Approximation of Functions and Their Applications [in Russian], Dnepropetrovsk University, Dnepropetrovsk (1975), pp. 82–89.

    Google Scholar 

  9. M. Sh. Shabozov, “On the error of interpolation by bilinear splines,” Ukr. Mat. Zh., 46, No.11, 1554–1560 (1994).

    Google Scholar 

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

    Google Scholar 

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Authors and Affiliations

  1. Ukrainian Academy of Customs Service, Dnepropetrovsk, Ukraine

    S. B. Vakarchuk & K. Yu. Myskin

Authors
  1. S. B. Vakarchuk
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  2. K. Yu. Myskin
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, No. 2, pp. 147–157, February, 2005.

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Vakarchuk, S.B., Myskin, K.Y. Some Problems of Simultaneous Approximation of Functions of Two Variables and Their Derivatives by Interpolation Bilinear Splines. Ukr Math J 57, 173–185 (2005). https://doi.org/10.1007/s11253-005-0180-0

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  • DOI: https://doi.org/10.1007/s11253-005-0180-0

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