关于B样条函数系的一个定理

A THEOREM OF B SPLINE FUNCTIONS

本文对于L.L.Schumaker的名著《Spline Functions:Basic Theory》第四章中关于B样条函数系线性无关的定理4.18的证明,指出了其欠妥当之处,提出了反例并给出了正确的证明。

In this paper, we point out that the proof of theorem 4.18 which is discussing linear inde. pendent of B spline functions in Chapter 4 of 'Spline Functions: Basic Theory' written by L. L. Schumaker, is unsuitable, we give a inverse example and a correct proof for this theorem.