Construction of interpolation splines minimizing the semi-norm in the space $K_2(P_m)$

Abstract

In the present paper, using S.L. Sobolev's method, interpolation spline that minimizes the expressionin the K 2 (Pm) space are constructed. Explicit formulas for the coefficients of the interpolation splines are obtained. The obtained interpolation spline is exact for monomials 1, x, x 2 , ..., x m−3 and for trigonometric functions sin ωx and cos ωx.