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
Yu. S. Zav’yalov, B. I. Kvasov, and V. L. Miroshnichenko, Methods of Spline Functions [in Russian], Nauka, Moscow (1980).
B. M. Shumilov, “On local approximation by bilinear splines,” Metody Splain-Funktsii (Vychislit. Sist.), Issue 81, 42–47 (1979).
V. N. Malozemov, “On polygonal interpolation,” Mat. Zametki, 1, No.5, 537–540 (1967).
S. B. Vakarchuk, “On interpolation by bilinear splines,” Mat. Zametki, 47, No.5, 26–30 (1990).
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).
N. P. Korneichuk, Splines in Approximation Theory [in Russian], Nauka, Moscow (1984).
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.
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.
M. Sh. Shabozov, “On the error of interpolation by bilinear splines,” Ukr. Mat. Zh., 46, No.11, 1554–1560 (1994).
Sh. E. Mikeladze, Numerical Methods of Mathematical Analysis [in Russian], Gostekhizdat, Moscow (1953).
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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