Past exam of the mathematics course of the University of Cambridge / 2004 / iii / Paper 71 / 4 / 2 / c / Solution

The general estimate from part 1 and the exact inverse norm from part 2b implyand in particular $\Vert P_x{\Vert }_{L^{\infty }}\le 2$, uniformly in the number of knots. This bound concerns the support-centred sites $x_i=i+3/2$; shifting the sampling sites changes the B-spline collocation matrix and can destroy uniform stability.