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Best approximation by ridge functions in $L_p$-spaces

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...

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Bibliographic Details
Date:	2010
Main Authors:	Maiorov, V. E., Майоров, В. Є.
Format:	Article
Language:	English
Published:	Institute of Mathematics, NAS of Ukraine 2010
Online Access:	https://umj.imath.kiev.ua/index.php/umj/article/view/2875
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Journal Title:	Ukrains’kyi Matematychnyi Zhurnal
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