Convergence analysis of an interpolation process for the derivatives of a complete spline

摘要

The question about the convergence of interpolation processes for the complete splines of odd degree and their derivatives is studied. The study is based on the representation of the spline derivatives in the bases of normalized and non-normalized B-splines. The systems of equations for the coefficients of such representations are obtained. The estimations of derivatives of the error function for the approximation of an interpolated function by the complete spline are established in terms of the norms of inverse matrices of the systems of equations. In particular, the C. de Boor's hypothesis (1975) on the unconditional convergence of the (n - 1)-th derivative of a complete (2n - 1)-degree spline is proved.