Absolute and relative cut-off in adaptive approximation by wavelets |
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Authors: | Claudio Canuto Anita Tabacco |
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Affiliation: | (1) Dipartimento di Matematica, Politecnico di Torino, C.so Duca degli Abruzzi 24, 10129 Torino, Italy |
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Abstract: | Given the wavelet expansion of a function v, a non-linear adaptive approximation of v is obtained by neglecting those coefficients whose size drops below a certain threshold. We propose several ways to define the threshold: all are based on the characterization of the local regularity of v (in a Sobolev or Besov scale) in terms of summability of properly defined subsets of its coefficients. A-priori estimates of the approximation error are derived. For the Haar system the asymptotic behavior of both the approximation error and the number of survived coefficients is thoroughly investigated for a class of functions having Hölder-type singularities. |
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