On an exponential-trigonometric natural interpolation spline
A.K. BoltaevV.I. Romanovskiy Institute of mathematics, Uzbekistan Academy of Sciences, University str. 4b, Tashkent 100174, UzbekistanD.M. AkhmedovV.I. Romanovskiy Institute of mathematics, Uzbekistan Academy of Sciences, University str. 4b, Tashkent 100174, Uzbekistan
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Аннотация
In the present paper, using the discrete analogue of the operator d8/dx8 + 2d4/dx4 + 1, an interpolation spline that minimizes the quantity ∫01(φIV(x)+φ(x))2dx in the Hilbert space W2(4,0) is constructed. Explicit formulas for the coefficients of the interpolation spline are obtained. The obtained interpolation spline is exact for the exponential-trigonometric functions e22xcos(22x),e22xsin(22x),e−22xcos(22x)and e−22xsin(22x). At the end of the paper we give some numerical results which confirm our theoretical results.
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