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N-term approximation in anisotropic function spaces

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

Standard

N-term approximation in anisotropic function spaces. / Hochmuth, Reinhard.
In: Mathematische Nachrichten, Vol. 244, No. 1, 2002, p. 131-149.

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

Harvard

Hochmuth, R 2002, 'N-term approximation in anisotropic function spaces', Mathematische Nachrichten, vol. 244, no. 1, pp. 131-149. https://doi.org/10.1002/1522-2616(200210)244:1<131::AID-MANA131>3.0.CO;2-G

APA

Hochmuth, R. (2002). N-term approximation in anisotropic function spaces. Mathematische Nachrichten, 244(1), 131-149. https://doi.org/10.1002/1522-2616(200210)244:1<131::AID-MANA131>3.0.CO;2-G

Vancouver

Hochmuth R. N-term approximation in anisotropic function spaces. Mathematische Nachrichten. 2002;244(1):131-149. doi: 10.1002/1522-2616(200210)244:1<131::AID-MANA131>3.0.CO;2-G

Bibtex

@article{44deaa15c3d54ab1aedce4b75ad64dad,
title = "N-term approximation in anisotropic function spaces",
abstract = "In L 2((0, 1) 2) infinitely many different biorthogonal wavelet bases may be introduced by taking tensor products of one-dimensional biorthogonal wavelet bases on the interval (0, 1). Most well-known are the standard tensor product bases and the hyperbolic bases. In [23, 24] further biorthogonal wavelet bases are introduced, which provide wavelet characterizations for functions in anisotropic Besov spaces. Here we address the following question: Which of those biorthogonal tensor product wavelet bases is the most appropriate one for approximating nonlinearly functions from anisotropic Besov spaces? It turns out, that the hyperbolic bases lead to nonlinear algorithms which converge as fast as the corresponding schemes with respect to specific anisotropy adapted bases. ",
keywords = "Mathematics, Anisotropic Besov spaces, Dominating mixed smoothness, Hyperbolic bases, N-term approximation, Tresholding, Wavelets",
author = "Reinhard Hochmuth",
year = "2002",
doi = "10.1002/1522-2616(200210)244:1<131::AID-MANA131>3.0.CO;2-G",
language = "English",
volume = "244",
pages = "131--149",
journal = "Mathematische Nachrichten",
issn = "1522-2616",
publisher = "Wiley-VCH Verlag",
number = "1",

}

RIS

TY - JOUR

T1 - N-term approximation in anisotropic function spaces

AU - Hochmuth, Reinhard

PY - 2002

Y1 - 2002

N2 - In L 2((0, 1) 2) infinitely many different biorthogonal wavelet bases may be introduced by taking tensor products of one-dimensional biorthogonal wavelet bases on the interval (0, 1). Most well-known are the standard tensor product bases and the hyperbolic bases. In [23, 24] further biorthogonal wavelet bases are introduced, which provide wavelet characterizations for functions in anisotropic Besov spaces. Here we address the following question: Which of those biorthogonal tensor product wavelet bases is the most appropriate one for approximating nonlinearly functions from anisotropic Besov spaces? It turns out, that the hyperbolic bases lead to nonlinear algorithms which converge as fast as the corresponding schemes with respect to specific anisotropy adapted bases.

AB - In L 2((0, 1) 2) infinitely many different biorthogonal wavelet bases may be introduced by taking tensor products of one-dimensional biorthogonal wavelet bases on the interval (0, 1). Most well-known are the standard tensor product bases and the hyperbolic bases. In [23, 24] further biorthogonal wavelet bases are introduced, which provide wavelet characterizations for functions in anisotropic Besov spaces. Here we address the following question: Which of those biorthogonal tensor product wavelet bases is the most appropriate one for approximating nonlinearly functions from anisotropic Besov spaces? It turns out, that the hyperbolic bases lead to nonlinear algorithms which converge as fast as the corresponding schemes with respect to specific anisotropy adapted bases.

KW - Mathematics

KW - Anisotropic Besov spaces

KW - Dominating mixed smoothness

KW - Hyperbolic bases

KW - N-term approximation

KW - Tresholding

KW - Wavelets

UR - http://www.scopus.com/inward/record.url?scp=0036402389&partnerID=8YFLogxK

U2 - 10.1002/1522-2616(200210)244:1<131::AID-MANA131>3.0.CO;2-G

DO - 10.1002/1522-2616(200210)244:1<131::AID-MANA131>3.0.CO;2-G

M3 - Journal articles

VL - 244

SP - 131

EP - 149

JO - Mathematische Nachrichten

JF - Mathematische Nachrichten

SN - 1522-2616

IS - 1

ER -

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Other publications by the same author(s)

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Göller, R. (Editor), Biehler, R., Hochmuth, R. K. & Rück, H.-G., 2017, Kassel: Kompetenzentrum Hochschuldidaktik Mathematik - Universität Kassel. 509 p. (khdm-Report; vol. 2017, no. 05)

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Hochmuth, R. K. & Schreiber, S., 2014, TeachING-LearnING.EU Tagungsband: movING Forward; Engineering Education from vision to mission. Tekkaya, A. E., Jeschke, S. & Petermann, M. (eds.). Technische Universität Dortmund, p. 68-76 9 p.

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Wassong, T., Frischemeier, D., Fischer, P. R., Hochmuth, R. & Bender, P., 2014, Wiesbaden: Springer Spektrum. 497 p.

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Liebendörfer, M., Hochmuth, R. K., Schreiber, S., Göller, R., Kolter, J., Biehler, R., Kortemeyer, J. & Ostsieker, L., 2014, Beiträge zum Mathematikunterricht 2014: Beiträge zur 48. Jahrestagung der Gesellschaft für Didaktik der Mathematik vom 10. bis 14. März 2014 in Koblenz. Roth, J. & Ames, J. (eds.). WTM - Verlag für wissenschaftliche Texte und Medien, Vol. 2. p. 739-742 4 p.

Research output: Contributions to collected editions/works › Article in conference proceedings › Research

Blended-Learning Brückenkurs Mathematik für Wirtschaftswissenschaftler.

Goguadze, G. & Hochmuth, R., 25.11.2013, Mathematik im Übergang Schule / Hochschule und im ersten Studienjahr: Extended Abstracts zur 2. khdm-Arbeitstagung. Hoppenbrock, A., Schreiber, S., Göller, R., Biehler, R., Büchler, B., Hochmuth, R. & Rück, H.-G. (eds.). Universitätsbibliothek Kassel, Vol. khdm-Report 13-01. p. 63-64 2 p. (KHDM-Report; vol. 13, no. 01).

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

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