Stability of the B-spline basis via knot insertion

We derive the stability inequality ‖C‖≤γ‖∑icibi‖ for the B-splines bi from the formula for knot insertion. The key observation is that knot removal increases the norm of the B-spline coefficients C={ci}i∈Z at most by a constant factor, which is independent of the knot sequence. As a consequence, stability for splines follows from the stability of the Bernstein basis.