Geodesic
Construction of interpolation splines minimizing the semi-norm in the space $K_2(P_m)$
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 11 (2018) no. 3, pp. 383-396

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In the present paper, using S.L. Sobolev's method, interpolation splines that minimize the expression $\int_0^1(\varphi^{(m)}(x)+\omega^2\varphi^{(m-2)}(x))^2dx$ in the space $K_2(P_m)$ are constructed. Explicit formulas for the coefficients of the interpolation splines are obtained. The obtained interpolation splines are exact for monomials $1,x,x^2,\dots, x^{m-3}$ and for trigonometric functions $\sin\omega x$ and $\cos\omega x$.
Keywords: Hilbert space, norm minimizing property, Sobolev's method, discrete argument function.
Mots-clés : interpolation spline 
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     author = {Abdullo R. Hayotov},
     title = {Construction of interpolation splines minimizing the semi-norm in the space $K_2(P_m)$},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {383--396},
     publisher = {mathdoc},
     volume = {11},
     number = {3},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2018_11_3_a14/}
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Abdullo R. Hayotov. Construction of interpolation splines minimizing the semi-norm in the space $K_2(P_m)$. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 11 (2018) no. 3, pp. 383-396. http://geodesic.mathdoc.fr/item/JSFU_2018_11_3_a14/