= Exact inverse norm of midpoint cubic spline collocation
{title2=$u_i=3\left[1-\frac{\rho^i+\rho^{n+1-i}}{1+\rho^{n+1}}\right],\quad\rho=2-\sqrt3$}
Conjugate the collocation <matrix> by the diagonal <matrix> with entries $(-1)^i$. The resulting negative-off-diagonal <matrix> has a nonnegative inverse, as a convergent <Neumann series> shows. The absolute inverse row sums are therefore the entries of its inverse applied to the all-ones vector. They solve $4u_i-u_{i-1}-u_{i+1}=6$ with $u_0=u_{n+1}=0$, whose solution is displayed. The maximum occurs at the central row or central two rows and equals the inverse <operator norm> on $\ell^\infty$. Consequently the associated <spline interpolation operator> has <norm> at most three independently of dimension.
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