American Journal of Numerical Analysis
ISSN (Print): 2372-2118 ISSN (Online): 2372-2126 Website: http://www.sciepub.com/journal/ajna Editor-in-chief: Emanuele Galligani
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American Journal of Numerical Analysis. 2014, 2(4), 107-114
DOI: 10.12691/ajna-2-4-3
Open AccessArticle

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

Kholmat M. Shadimetov1, 2, Abdullo R. Hayotov1, and Azamov S. Siroj1

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

2Tashkent Institute of Railway Engineers, Tashkent, Uzbekistan

Pub. Date: May 26, 2014

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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