Article ID Journal Published Year Pages File Type
4607985 Journal of Approximation Theory 2009 13 Pages PDF
Abstract

We consider relative widths characterizing the best approximation of a fixed set by its sections of given dimension. For Sobolev classes Wp1 on [0,1][0,1] with restriction f(0)=0f(0)=0, we determine the exact orders of such widths in the spaces LqLq for 1≤q≤p≤∞1≤q≤p≤∞. We also obtain the exact values of the corresponding relative widths for p=q=1,1≤q≤p=2p=q=1,1≤q≤p=2 and p=q=∞p=q=∞.

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Physical Sciences and Engineering Mathematics Analysis
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