On the best approximation by ridge functions in the uniform norm
GORDON, Y ; Maiorov, V ; Meyer, Mathieu ; REISNER, S
HAL, hal-00693663 / Harvested from HAL
Text on HAL
We consider the best approximation of some function classes by the manifold M-n consisting of sums of n arbitrary ridge functions. It is proved that the deviation of the Sobolev class W-p(r,d) from the manifold M-n in the space L-q for any 2 less than or equal to q less than or equal to p less than or equal to infinity behaves asymptotically as n(-r/(d-1)). In particular, we obtain this asymptotic estimate for the uniform norm p = q = infinity.
Publié le : 2002-07-05
Classification:  [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph] 
@article{hal-00693663,
     author = {GORDON, Y and Maiorov, V and Meyer, Mathieu and REISNER, S},
     title = {On the best approximation by ridge functions in the uniform norm},
     journal = {HAL},
     volume = {2002},
     number = {0},
     year = {2002},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00693663}
}

GORDON, Y; Maiorov, V; Meyer, Mathieu; REISNER, S. On the best approximation by ridge functions in the uniform norm. HAL, Tome 2002 (2002) no. 0, . http://gdmltest.u-ga.fr/item/hal-00693663/