Stability of the B-spline basis via knot insertion

We derive the stability inequality parallel to C parallel to less than or e qual to gamma parallel to Sigma(i) c(i)b(i) parallel to for the B-splines b (i) from the formula for knot insertion. The key observation is that knot r emoval increases the norm of the B-spline coefficients C = {c(i)}(i is an e lement of Z) at most by a constant factor, which is independent of the knot sequence. As a consequence, stability for splines follows from the stabili ty of the Bernstein basis. (C) 2000 Elsevier Science B.V. All rights reserv ed.