Abstract
We introduce a definition of nonlinear n-widths and then determine the n-widths of the unit ball of the Sobolev spaceW r p inL 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.
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This author was supported by NSF Grant DMS 8620108
This author was supported by NSF Grant DMS 8803585
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DeVore, R.A., Howard, R. & Micchelli, C. Optimal nonlinear approximation. Manuscripta Math 63, 469–478 (1989). https://doi.org/10.1007/BF01171759
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DOI: https://doi.org/10.1007/BF01171759