method is best from a purely mathematical point of view or if it is su ciently fast from ... natural cubic spline with the knots determined in the second step (we note.
Cubic spline data reduction choosing the knots from a third derivative criterion
C. Conti, R. Morandi, C. Rabut and A. Sestini Abstract.
This paper presents a data reduction method for functional data. Starting with noisy or not noisy data, we rst de ne a function f , called the \reference function", as a cubic smoothing spline function is then by using a criterion based on least{squares spline approximating all the data is derived with these knots. Numerical results show the e ectiveness of the method.
x1. Introduction
For a given set of N + 1 noisy or not noisy data (xi; yi )i=0;:::;N , data reduction using polynomial splines consists in determining a polynomial spline function with some assigned degree and having n + 1 knots (j )j=0;:::;n, with n
