2017
Том 69
№ 6

All Issues

Best approximation by ridge functions in $L_p$-spaces

Maiorov V. E.

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Abstract

We study the approximation of the classes of functions by the manifold $R_n$ formed by all possible linear combinations of $n$ ridge functions of the form $r(a · x))$. It is proved that, for any $1 ≤ q ≤ p ≤ ∞$, the deviation of the Sobolev class $W^r_p$ from the set $R_n$ of ridge functions in the space $L_q (B^d)$ satisfies the sharp order $n^{-r/(d-1)}$.

English version (Springer): Ukrainian Mathematical Journal 62 (2010), no. 3, pp 452-466.

Citation Example: Maiorov V. E. Best approximation by ridge functions in $L_p$-spaces // Ukr. Mat. Zh. - 2010. - 62, № 3. - pp. 396–408.

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