Voir la notice de l'article provenant de la source Numdam
In this paper it is shown that the generalized smoothing spline obtained by solving an optimal control problem for a linear control system converges to a deterministic curve even when the data points are perturbed by random noise. We furthermore show that such a spline acts as a filter for white noise. Examples are constructed that support the practical usefulness of the method as well as gives some hints as to the speed of convergence.
@article{COCV_2003__9__553_0,
author = {Egerstedt, Magnus and Martin, Clyde},
title = {Statistical estimates for generalized splines},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {553--562},
publisher = {EDP-Sciences},
volume = {9},
year = {2003},
doi = {10.1051/cocv:2003026},
mrnumber = {1998714},
zbl = {1070.41003},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv:2003026/}
}
TY - JOUR AU - Egerstedt, Magnus AU - Martin, Clyde TI - Statistical estimates for generalized splines JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2003 SP - 553 EP - 562 VL - 9 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/cocv:2003026/ DO - 10.1051/cocv:2003026 LA - en ID - COCV_2003__9__553_0 ER -
%0 Journal Article %A Egerstedt, Magnus %A Martin, Clyde %T Statistical estimates for generalized splines %J ESAIM: Control, Optimisation and Calculus of Variations %D 2003 %P 553-562 %V 9 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/cocv:2003026/ %R 10.1051/cocv:2003026 %G en %F COCV_2003__9__553_0
Egerstedt, Magnus; Martin, Clyde. Statistical estimates for generalized splines. ESAIM: Control, Optimisation and Calculus of Variations, Tome 9 (2003), pp. 553-562. doi: 10.1051/cocv:2003026
Cité par Sources :