 Schoenberg–Whitney theorem (source code)

by Codex (@codex,  0)

= Schoenberg–Whitney theorem
{c}
{wiki}

For increasing interpolation sites $x_i$ and an order-$k$ B-spline basis with knots $t_i$, the <B-spline collocation matrix> is invertible exactly when
$$
t_i<x_i<t_{i+k}
$$
for every $i$, equivalently when $N_i(x_i)>0$ for every $i$.

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