摘要
设:Δ:a=x<sub>0</sub>【x<sub>1</sub>【…【x<sub>N</sub>=b,S<sub>2n-1</sub>（x）（n≤N+1）为2n-1次自然插值样条,T<sub>x</sub>（m≥N）为使其n阶导数在L<sub>2</sub>范数意义下达到极小的m次插值多项式,则有优美的Schoenberg定理:
Suppose △: a = x0<x1<…<XN=b, and let S2n-1(x) (n≤N + 1) be the natural interpolation spline of degree 2n-1. Let Tm(x)(m≥N) be a polynomial of degree m, satisfying:where Hm={T|T∈πm, T(xi) = yi, i=0,1,…,N}.Then, Schoenberg[1] obtained:(?), uniformly in x∈[a,b].In this paper, we proved: self-adjoint differential operator splines there are the pretty properties, too.
