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Restricted nonlinear approximation

Research output: Journal contributions › Journal articles › Research › peer-review

Standard

Restricted nonlinear approximation. / Cohen, Albert; DeVore, Ronald A.; Hochmuth, Reinhard.
In: Constructive Approximation, Vol. 16, No. 1, 01.01.2000, p. 85-113.

Research output: Journal contributions › Journal articles › Research › peer-review

Harvard

Cohen, A, DeVore, RA & Hochmuth, R 2000, 'Restricted nonlinear approximation', Constructive Approximation, vol. 16, no. 1, pp. 85-113. https://doi.org/10.1007/s003659910004

APA

Cohen, A., DeVore, R. A., & Hochmuth, R. (2000). Restricted nonlinear approximation. Constructive Approximation, 16(1), 85-113. https://doi.org/10.1007/s003659910004

Vancouver

Cohen A, DeVore RA, Hochmuth R. Restricted nonlinear approximation. Constructive Approximation. 2000 Jan 1;16(1):85-113. doi: 10.1007/s003659910004

Bibtex

@article{f245a697e96b41ca93ca6c43049d4eae,
title = "Restricted nonlinear approximation",
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 = "Mathematics, Besov spaces, Characterization of approximation classes, K -functional, Nonlinear approximation, Restricted approximation, AMS Classification. 41, 41A17, 41A25, 41A46.",
author = "Albert Cohen and DeVore, {Ronald A.} and Reinhard Hochmuth",
year = "2000",
month = jan,
day = "1",
doi = "10.1007/s003659910004",
language = "English",
volume = "16",
pages = "85--113",
journal = "Constructive Approximation",
issn = "0176-4276",
publisher = "Springer",
number = "1",

}

RIS

TY - JOUR

T1 - Restricted nonlinear approximation

AU - Cohen, Albert

AU - DeVore, Ronald A.

AU - Hochmuth, Reinhard

PY - 2000/1/1

Y1 - 2000/1/1

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 - Mathematics

KW - Besov spaces

KW - Characterization of approximation classes

KW - K -functional

KW - Nonlinear approximation

KW - Restricted approximation

KW - AMS Classification. 41, 41A17, 41A25, 41A46.

UR - http://www.scopus.com/inward/record.url?scp=0034354926&partnerID=8YFLogxK

U2 - 10.1007/s003659910004

DO - 10.1007/s003659910004

M3 - Journal articles

VL - 16

SP - 85

EP - 113

JO - Constructive Approximation

JF - Constructive Approximation

SN - 0176-4276

IS - 1

ER -

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Research output: Contributions to collected editions/works › Other › Research

DOI