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Information Center for Mathematical Science

논문검색

Information Center for Mathematical Science

논문검색

Manuscripta Mathematica.
( Vol. 63 NO.3 / (1989))
Optimal Nonlinear Approximation
Ronald A. DeVore, Ralph Howard, Charles Micchelli,
Pages. 469-478
Abstract 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 $L_p$. 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.
Contents 1. Introduction 2. Remarks on the definition of $d_n$ 3. A lower bound for $d_n$ 4. Lower bounds for widths of smoothness classes 5. Upper bounds for $d_n(K)_X$
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