Restricted nonlinear approximation
- authored by
- A. Cohen, R. A. DeVore, R. Hochmuth
- Abstract
We introduce a new form of nonlinear approximation called restricted approximation. It is a generalization of n-term wavelet approximation in which a weight function is used to control the terms in the wavelet expansion of the approximant. This form of approximation occurs in statistical estimation and in the characterization of interpolation spaces for certain pairs of Lp and Besov spaces. We characterize, both in terms of their wavelet coefficients and also in terms of their smoothness, the functions which are approximated with a specified rate by restricted approximation. We also show the relation of this form of approximation with certain types of thresholding of wavelet coefficients.
- External Organisation(s)
-
Universite Paris 6
University of South Carolina
Freie Universität Berlin (FU Berlin)
- Type
- Article
- Journal
- Constructive approximation
- Volume
- 16
- Pages
- 85-113
- No. of pages
- 29
- ISSN
- 0176-4276
- Publication date
- 2000
- Publication status
- Published
- Peer reviewed
- Yes
- ASJC Scopus subject areas
- Analysis, General Mathematics, Computational Mathematics
- Electronic version(s)
-
https://doi.org/10.1007/s003659910004 (Access:
Unknown)
-
Details in the research portal "Research@Leibniz University"
