Approximation of some classes of functions of many variables by harmonic splines
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We determine the exact values of the upper bounds of the errors of approximation by harmonic splines for functions u defined on an n-dimensional parallelepiped Ω and such that ||Δu|| L∞(Ω) ≤ 1 and functions u defined on Ω and such that ||Δu|| L∞(Ω) ≤ 1, 1 ≤ p ≤ ∞. In the first case, the error is estimated in L p (Ω). 1 ≤ p ≤ ∞. In the second case, the error is estimated in L 1(Ω).
KeywordsGreen Function Interpolation Polynomial Arbitrary Solution Piecewise Polynomial Function Polyhedral Function
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- 2.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 polyhedral functions and spline functions in the uniform metric,” in: Investigations of the Contemporary Problems of Summation and Approximation of Functions and Their Applications [in Russian], Dnepropetrovsk (1975), pp. 82–89.Google Scholar
- 12.V. F. Babenko and T. Yu. Leskevich, “Error of interpolation of some classes of functions by multilinear splines,” Visn. Dnipropetr. Univ., Ser. Mat., 18, No. 6/1, 28–37 (2010).Google Scholar
- 15.V. Hoppe, “Finite elements with harmonic interpolation functions,” in: J. R. Whiteman (editor), Proceedings of the Conference on Mathematics of Finite Elements and Applications, Academic Press, London (1973), pp. 131–142.Google Scholar
- 16.D. R. Richtmyer, Principles of Advanced Mathematical Physics [Russian translation], Mir, Moscow (1982).Google Scholar
- 17.O. A. Oleinik, Lectures on Partial Differential Equations [in Russian], BINOM, Moscow (2005).Google Scholar