Algorithms and error bounds for multivariate piecewise constant approximation

Oleg Davydov

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Abstract

We review the surprisingly rich theory of approximation of functions of many vari-
ables by piecewise constants. This covers for example the Sobolev-Poincar´e inequalities, parts of the theory of nonlinear approximation, Haar wavelets and tree approximation, as well as recent results about approximation orders achievable on anisotropic partitions.
Original languageEnglish
Title of host publicationApproximation Algorithms for Complex Systems
Subtitle of host publicationSpringer Proceedings in Mathematics 2011
EditorsEmmanuil H Georgoulis, Armin Iske, Jeremy Levesley
Place of PublicationHeidelberg
PublisherSpringer-Verlag
Pages27-45
Number of pages19
Volume3
Edition1
ISBN (Print)9783642168758
DOIs
Publication statusPublished - 2011
Event6th International Conference on Algorithms for Approximation - Ambleside, United Kingdom
Duration: 31 Aug 20094 Sep 2009

Conference

Conference6th International Conference on Algorithms for Approximation
CountryUnited Kingdom
CityAmbleside
Period31/08/094/09/09

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Keywords

  • variables
  • piecewise constants
  • algorithms
  • Sobolev-Poincaré inequalities
  • Haar wavelets
  • tree approximation

Cite this

Davydov, O. (2011). Algorithms and error bounds for multivariate piecewise constant approximation. In E. H. Georgoulis, A. Iske, & J. Levesley (Eds.), Approximation Algorithms for Complex Systems: Springer Proceedings in Mathematics 2011 (1 ed., Vol. 3, pp. 27-45). Heidelberg: Springer-Verlag. https://doi.org/10.1007/978-3-642-16876-5_2