= Centered quadratic spline interpolation
{title2=$A=\tfrac18\operatorname{tridiag}(1,6,1),\quad\|A^{-1}\|_\infty<2$}
For unit-spaced order-three <B-splines> sampled at <support> midpoints $i+3/2$, the <B-spline collocation matrix> has diagonal $3/4$ and neighboring entries $1/8$. Conjugating by alternating diagonal signs reduces its inverse absolute values to the nonnegative inverse of $\operatorname{tridiag}(-1,6,-1)/8$. With $\tau=3-2\sqrt2$, the absolute row sums are $r_i=2[1-(\tau^i+\tau^{n+1-i})/(1+\tau^{n+1})]$. This follows by solving $6r_i-r_{i-1}-r_{i+1}=8$ with $r_0=r_{n+1}=0$. The maximum occurs at the middle row or rows and tends to two as $n$ grows. Nonnegativity and subpartition of unity of the <B-splines> transfer this bound to the <spline interpolation operator>.
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