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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
Keywords:
spline; division
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