= B-spline interpolation operator norm
{c}
{title2=$d_k^{-1}\|A^{-1}\|_{\ell^\infty}\le\|P\|_\infty\le\|A^{-1}\|_{\ell^\infty}$}
For distinct interpolation sites and an invertible <B-spline collocation matrix>, the interpolant is $P=BA^{-1}R$, where $R$ samples data and $Ba=\sum_i a_iN_i$. Sampling and basis synthesis have <operator norms> at most one in the <supremum norm>. For the reverse inequality, realize the signs of a maximal absolute row sum of $A^{-1}$ as values of a continuous function of norm one, and apply <uniform-norm stability of a B-spline basis>. This yields both displayed bounds.
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