Numerische Mathematik

, Volume 34, Issue 1, pp 15-28

First online:

Sur le choix du paramètre d'ajustement dans le lissage par fonctions spline

  • F. Utreras DiazAffiliated withUniversité Scientifique et Médicale Laboratoire de Mathématiques Appliquées

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On the choice of the smoothing parameter in the smoothing of noisy data by spline functions


We consider the problem of approximating an unknown functionf, known with error atn equally spaced points of the real interval [a, b].

To solve this problem, we use the natural polynomial smoothing splines. We show that the eigenvalues associated to these splines converge to the eigenvalues of a differential operator and we use this fact to obtain an algorithm, based on the Generalized Cross Validation method, to calculate the smoothing parameter.

With this algorithm, we divide byn the time used by classical methods.

Subject Classifications

AMS(MOS): 65D10, 65D07