Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 318 / 3 / c / Solution

For Cardinal cubic B-splines, the values at integer knots areand all other knot values vanish. Since $x_i=t_{i+2}$,This tridiagonal matrix is strictly diagonally dominant. The standard inverse bound for such a matrix givesThe minimum denominator is $4/6-2/6=1/3$, soPart (b) then yields