Abstract
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 L p-spaces. All the bounds are based on a simple identity for divided differences.
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Lyche, T., Mørken, K. The Sensitivity of a Spline Function to Perturbations of the Knots. BIT Numerical Mathematics 39, 305–322 (1999). https://doi.org/10.1023/A:1022346030560
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DOI: https://doi.org/10.1023/A:1022346030560