RMC - Vol. 4, Num. 2, 3 - M. C. López de Silanes/R. Arcangéli

Full paper in PDF:
$% M. C. López de Silanes and R. Arcangéli, Sur la convergence de D^m-splines d’ajustement pour des données exactes ou bruitées, Rev. Mat. Univ. Complut. Madrid 4 (1991), no. 2, 3, 279–294.%$

Sur la convergence de D^m-splines d’ajustement pour des données exactes ou bruitées

María Cruz LÓPEZ DE SILANES and Rémi ARCANGÉLI

Departamento de Matemática Aplicada, CPS Calle María de Luna, 3 E-50015 Zaragoza — Spain	Laboratoire de Mathématiques Apliquées URA CNRS 1204, Université de Pau Avenue de l’Université F-64000 Pau — France

Received: September 3, 1990

ABSTRACT

Let $_O_$ be a bounded open subset of $n R$ containing the data points, $d$ the Hausdorff distance from the set of data points to $_O_$ and $e$ the smoothing parameter. Assume that $-n e= o(d )$ , $d --> 0$ , and in addition when the data are noisy, that the “white noise” hypothesis is satisfied. Then, for smoothing of exact or noisy data with $m D$ -splines, convergence and error estimates results are obtained. These results improve previous ones given by F. Utreras or the authors.

1991 Mathematics Subject Classification: 41A15.