1. //
  2. Start
  3. //
  4. Publikationen
  5. N-term approximation in anisotropic func...
  6. Formate
  7. //

N-term approximation in anisotropic function spaces

Publikation: Beiträge in Zeitschriften › Zeitschriftenaufsätze › Forschung › begutachtet

Standard

N-term approximation in anisotropic function spaces. / Hochmuth, Reinhard.
in: Mathematische Nachrichten, Jahrgang 244, Nr. 1, 2002, S. 131-149.

Publikation: Beiträge in Zeitschriften › Zeitschriftenaufsätze › Forschung › begutachtet

Harvard

Hochmuth, R 2002, 'N-term approximation in anisotropic function spaces', Mathematische Nachrichten, Jg. 244, Nr. 1, S. 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 -

In der gleichen Zeitschrift

Anisotropic wavelet bases and thresholding

Hochmuth, R., 2007, in: Mathematische Nachrichten. 280, 5-6, S. 523-533 11 S.

Publikation: Beiträge in Zeitschriften › Zeitschriftenaufsätze › Forschung › begutachtet

The Cox ring of the space of complete rank two collineations

Hausen, J. & Liebendörfer, M., 06.2012, in: Mathematische Nachrichten. 285, 8-9, S. 974-980 7 S.

Publikation: Beiträge in Zeitschriften › Zeitschriftenaufsätze › Forschung › begutachtet

Weitere Publikationen dieser Person(en)

Didactics of Mathematics in Higher Education as a Scientific Discipline - Conference Proceedings

Göller, R. (Herausgeber*in), Biehler, R., Hochmuth, R. K. & Rück, H.-G., 2017, Kassel: Kompetenzentrum Hochschuldidaktik Mathematik - Universität Kassel. 509 S. (khdm-Report; Band 2017, Nr. 05)

Publikation: Bücher und Anthologien › Konferenzbände und -dokumentationen › Forschung

Mathematik im Ingenieurwissenschaftsstudium – Ansätze zu einer fachbezogenen Kompetenzmodellierung

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. (Hrsg.). Technische Universität Dortmund, S. 68-76 9 S.

Publikation: Beiträge in Sammelwerken › Aufsätze in Konferenzbänden › Forschung › begutachtet

Mit Werkzeugen Mathematik und Stochastik lernen

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

Publikation: Bücher und Anthologien › Buch

Vorstellung eines Fragebogens zur Erfassung von Lernstrategien in mathematikhaltigen Studiengängen.

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. (Hrsg.). WTM - Verlag für wissenschaftliche Texte und Medien, Band 2. S. 739-742 4 S.

Publikation: Beiträge in Sammelwerken › Aufsätze in Konferenzbänden › Forschung

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. (Hrsg.). Universitätsbibliothek Kassel, Band khdm-Report 13-01. S. 63-64 2 S. (KHDM-Report; Band 13, Nr. 01).

Publikation: Beiträge in Sammelwerken › Andere (Vor- und Nachworte ...) › Forschung

DOI

Zuletzt angesehen

Aktivitäten

  1. Interstitial spaces as garbage cans of field transformation where problems and solutions meet: the case of blockchain and music cross-fertilization
  2. Big Data, Data Trading, and Data Protection
  3. A utilitarian notion of responsibility for sustainability
  4. Responding ASAP? The Role of Age in Dealing with Availability and Response Expectations
  5. Eine Podiumsdiskussion zu Fracking
  6. Negotiating normativity: discourses of (non) belonging and (non) coincidences in the context of transnational adoption
  7. German Teaching and Learning Materials - Lifelong Learning and Competency-Based Instruction
  8. 'Can you play a new CD,please?' Speech act representation in EFL textbooks: An interlanguage pragmatic appraisal (Universität Gießen, invited talk)
  9. What if Civilization Collapses? Management Scholarship in and for Deep Adaption
  10. Can we solve the climate crisis? Contributions from artS, technology and science
  11. WK ORG Workshop - WK ORG 2019
  12. How to make use of evidence based management in entrepreneurship: The example of Personal Initiative Training
  13. Effective working hours and wages: the case of downward adjustment via paid absenteeism
  14. Collective Decisions
  15. “Visual Rhetoric as a three-dimensional practice”
  16. Licht im Dunkeln 2005
  17. 5th European Conference of Apidology - EurBee 2012
  18. Reactivity on a student-centered recording system – a video-based longitudinal study in primary education
  19. Tolerating and inducing temporal asynchronicity in complex innovation journeys
  20. Personal care products as source for micropollutants in Greywater-Identification, quantification and on-site treatment
  21. Sustainability Reporting on the World Wide Web: Developments in Germany
  22. Applied Vegetation Science (Zeitschrift)
  23. Universität Zürich
  24. Deferred Compensation Schemes, Fairness Concerns, and Employment of Older Workers
  25. Forschungspraxis und Selbstsorge in Sensitive Research
  26. Biological Oxidation of Iron with Various Oxidants.
  27. Purpuseful Work Symposium

Publikationen

  1. Generating Energy Optimal Powertrain Force Trajectories with Dynamic Constraints
  2. Functional Richness and Relative Resilience of Bird Communities in Regions with Different Land Use Intensities
  3. Erroneous examples as desirable difficulty
  4. Modelling, Simulation and Experimental Analysis of a Metal-Polymer Hybrid Fibre based Microstrip Resonator for High Frequency Characterisation
  5. Comparing two hybrid neural network models to predict real-world bus travel time
  6. Gamma GAMM applied on tree growth data
  7. Fallstudie
  8. A holistic view on security and collaboration in safe space
  9. Thanking and responding to thanks in American English: Language patterning and contextual appropriateness
  10. From estimation results to stylized facts
  11. Learning how to request using textbooks
  12. Mitarbeitergespräch
  13. Determinants of Credit Allocation for Photovoltaic Projects
  14. Intra- and interspecific tree diversity promotes multitrophic plant–Hemiptera–ant interactions in a forest diversity experiment