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Journal Articles Constructive Approximation Year : 2002

On the best approximation by ridge functions in the uniform norm

Mathieu Meyer
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S Reisner
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Abstract

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.
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Dates and versions

hal-00693663 , version 1 (02-05-2012)

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  • HAL Id : hal-00693663 , version 1

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Y Gordon, V Maiorov, Mathieu Meyer, S Reisner. On the best approximation by ridge functions in the uniform norm. Constructive Approximation, 2002, 18 (1), pp.61--85. ⟨hal-00693663⟩
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