Stability of the B-spline basis via knot insertion
We derive the stability inequality parallel to C parallel to less than or equal 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 removal increases the norm of the B-spline coefficients C = {c(i)}(i is an element of 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. (C) 2000 Elsevier Science B.V. All rights reserved.
stability b-splines knot insertion