= Linear growth of shifted quadratic spline interpolation
{title2=$2n/3\le\|P_n\|_\infty\le2n$}
For the degree-two <Cardinal B-spline> basis on knots $1,\ldots,n+3$, sampling at $x_i=i+2$ gives the upper-bidiagonal <B-spline collocation matrix> $A=(I+S)/2$, where $S$ is the one-step upper shift. Since $S^n=0$, $A^{-1}=2\sum_{r=0}^{n-1}(-S)^r$ and its maximum absolute row sum is $2n$. The <B-spline interpolation operator norm> estimate with the order-three stability constant $d_3=3$ gives the displayed linear upper and lower bounds. The lower bound proves failure of uniform boundedness.
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