Construction of DmDm-splines in L2(m)(0,1) space by Sobolev method

In the present paper, using S.L. Sobolev’s method, interpolation DmDm-splines that minimizes the expression ∫01(φ(m)(x))2dx in the L2(m)(0,1) space are constructed. Explicit formulas for the coefficients of the interpolation splines are obtained. The obtained interpolation spline is exact for polynomials of degree m-1m-1. Some numerical experiments are presented. Moreover the connection between the obtained interpolation splines and the optimal quadrature formulas are shown.