The sensitivity of a spline function to perturbations of the knots
The authors study the bounds for the difference between a primary spline and a secondary spline with the same B-spline coefficients, but different knots. It is shown that a continuous spline and its derivatives depend continuously on the knots in any \(L^p\)-space, \(p \geq 1\), while a discontinuous spline is only Lipshitz continuous with exponent \({1} \over {p}\) in \(L^p\). The authors also show that the results can be extended for parametric spline curves.
scientific article; zbMATH DE number 1309455