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Approximation of functions of two variables by harmonic splines

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Abstract

We construct two-dimensional splines and give two versions of an estimate of the deviation of splines from approximated functions. We compare approximations by a planar broken line and by a harmonic spline. We also substantiate the advisability of introduction of the notion of harmonic splines in mathematics.

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References

  1. V. S. Vladimirov,Equations of Mathematical Physics [in Russian], Nauka, Moscow (1967).

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  2. I. S. Gradshtein and I. M. Ryzhik,Tables of Integrals, Sums, Series, and Products [in Russian], Nauka, Moscow (1963).

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Deceased.

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 9, pp. 1190–1196, September, 1995.

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Klimenko, V.T. Approximation of functions of two variables by harmonic splines. Ukr Math J 47, 1356–1363 (1995). https://doi.org/10.1007/BF01057510

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  • DOI: https://doi.org/10.1007/BF01057510

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