eng Science and Education Publishing American Journal of Numerical Analysis 2328-7292 2014-05-26 2 4 107 114 10.12691/ajna-2-4-3 AJNA2014243 article Kholmat M. Shadimetov 1 2 Abdullo R. Hayotov hayotov@mail.ru 2 Azamov S. Siroj 2 Institute of Mathematics, National University of Uzbekistan, Tashkent, Uzbekistan 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). http://pubs.sciepub.com/ajna/2/4/3/ajna-2-4-3.pdf interpolation spline Hilbert space the norm minimizing property SL Sobolev's method discrete argument function