The sensitivity of a spline function to perturbations of the knots

In this paper we study the sensitivity of a spline function, represented in terms of B-splines, to perturbations of the knots. We do this by bounding the difference between a primary spline and a secondary spline with the same B-spline coefficients, but different knots. We give a number of bounds for this difference, both local bounds and global bounds in general LP-spaces. All the bounds are based on a simple identity for divided differences. AMS subject classification: 41A15.