Stability of the B-spline basis via knot insertion

We derive the stability inequality C i cibi 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}iZ 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.

• Type: Journal
• Year: 2000
• Where: CAGD
• Authors: Klaus Höllig
• Keywords: B-splines Bi, CAGD 2000, Knot, Stability Inequality