Details
| Original language | English |
|---|---|
| Pages (from-to) | 85-113 |
| Number of pages | 29 |
| Journal | Constructive approximation |
| Volume | 16 |
| Issue number | 1 |
| Publication status | Published - 2000 |
| Externally published | Yes |
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.
Keywords
- Besov spaces, Characterization of approximation classes, K -functional, Nonlinear approximation, Restricted approximation
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Mathematics(all)
- General Mathematics
- Mathematics(all)
- Computational Mathematics
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In: Constructive approximation, Vol. 16, No. 1, 2000, p. 85-113.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Restricted nonlinear approximation
AU - Cohen, A.
AU - DeVore, R. A.
AU - Hochmuth, R.
PY - 2000
Y1 - 2000
N2 - 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.
AB - 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.
KW - Besov spaces
KW - Characterization of approximation classes
KW - K -functional
KW - Nonlinear approximation
KW - Restricted approximation
UR - http://www.scopus.com/inward/record.url?scp=0034354926&partnerID=8YFLogxK
U2 - 10.1007/s003659910004
DO - 10.1007/s003659910004
M3 - Article
AN - SCOPUS:0034354926
VL - 16
SP - 85
EP - 113
JO - Constructive approximation
JF - Constructive approximation
SN - 0176-4276
IS - 1
ER -