Restricted nonlinear approximation

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Autoren

Externe Organisationen

  • Université Paris 6
  • University of South Carolina
  • Freie Universität Berlin (FU Berlin)
Forschungs-netzwerk anzeigen

Details

OriginalspracheEnglisch
Seiten (von - bis)85-113
Seitenumfang29
FachzeitschriftConstructive approximation
Jahrgang16
Ausgabenummer1
PublikationsstatusVeröffentlicht - 2000
Extern publiziertJa

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.

ASJC Scopus Sachgebiete

Zitieren

Restricted nonlinear approximation. / Cohen, A.; DeVore, R. A.; Hochmuth, R.
in: Constructive approximation, Jahrgang 16, Nr. 1, 2000, S. 85-113.

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Cohen A, DeVore RA, Hochmuth R. Restricted nonlinear approximation. Constructive approximation. 2000;16(1):85-113. doi: 10.1007/s003659910004
Cohen, A. ; DeVore, R. A. ; Hochmuth, R. / Restricted nonlinear approximation. in: Constructive approximation. 2000 ; Jahrgang 16, Nr. 1. S. 85-113.
Download
@article{6947c58596ba44d29ecd3e9047bd010b,
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 = "Besov spaces, Characterization of approximation classes, K -functional, Nonlinear approximation, Restricted approximation",
author = "A. Cohen and DeVore, {R. A.} and R. Hochmuth",
year = "2000",
doi = "10.1007/s003659910004",
language = "English",
volume = "16",
pages = "85--113",
journal = "Constructive approximation",
issn = "0176-4276",
publisher = "Springer New York",
number = "1",

}

Download

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 -

Von denselben Autoren