Interpolation Splines Minimizing Semi-Norm in K₂(P₂) Space

Kholmat M. Shadimetov^{1, 2}, Abdullo R. Hayotov^1, and Azamov S. Siroj¹

¹Institute of Mathematics, National University of Uzbekistan, Tashkent, Uzbekistan

²Tashkent Institute of Railway Engineers, Tashkent, Uzbekistan

Cite this paper:
Kholmat M. Shadimetov, Abdullo R. Hayotov and Azamov S. Siroj. Interpolation Splines Minimizing Semi-Norm in K₂(P₂) Space. American Journal of Numerical Analysis. 2014; 2(4):107-114. doi: 10.12691/ajna-2-4-3

Abstract

In the present paper using S.L. Sobolev’s method interpolation splines minimizing the semi-norm in K₂(P₂) space are constructed. Explicit formulas for coefficients of interpolation splines are obtained. The obtained interpolation spline is exact for the functions and . Also we give some numerical results where we showed connection between optimal quadrature formula and obtained interpolation spline in the space K₂(P₂).

Keywords:
interpolation spline Hilbert space the norm minimizing property S.L. Sobolev’s method discrete argument function

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