On an exponential-trigonometric natural interpolation spline

On an exponential-trigonometric natural interpolation spline

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 i...

Ausführliche Beschreibung

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Bibliographische Detailangaben
Hauptverfasser: Boltaev, Aziz, Akhmedov, Dilshod
Format: Tagungsbericht
Sprache:eng
Schlagworte:
Hilbert space
Interpolation
Operators (mathematics)
Trigonometric functions
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Beschreibung
Zusammenfassung: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.
ISSN:0094-243X
1551-7616
DOI:10.1063/5.0057116