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A fundamental property of $$B$$-splines. (English) Zbl 1052.65508
Summary: Let $$\Delta_n\colon t_0\leq t_1 \leq \dots t_n$$ be a division on the real line, where $$n\in {\mathbb N}^*$$ and $$t_0, t_1, \dots, t_n\in {\mathbb R}$$. We denote by $$B_{i, k}(x)$$, $$k=0, \dots, n-1$$, $$i=0, \dots, n-1-k$$, $$x\in {\mathbb R}$$, the functions $$B$$-spline corresponding to the division $$\Delta_n$$. Our aim here is to prove a new fundamental property of $$b$$-splines.
##### MSC:
 65D07 Numerical computation using splines
spline; division
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