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Optimal nonlinear approximation. (English) Zbl 0682.41033

Summary: We introduce a definition of nonlinear n-widths and then determine the n- widths of the unit ball of the Sobolev space \(W^ r_ p\) in \(L_ q\). We prove that in the sense of these widths the manifold of splines of fixed degree with n free knots is optimal for approximating functions in these Sobolev spaces.

MSC:

41A46 Approximation by arbitrary nonlinear expressions; widths and entropy
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References:

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