Algorithms and error bounds for multivariate piecewise constant approximation

Oleg Davydov

doi:10.1007/978-3-642-16876-5_2

Algorithms and error bounds for multivariate piecewise constant approximation

Oleg Davydov

Mathematics And Statistics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution book

5 Citations (Scopus)

84 Downloads (Pure)

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 language	English
Title of host publication	Approximation Algorithms for Complex Systems
Subtitle of host publication	Springer Proceedings in Mathematics 2011
Editors	Emmanuil H Georgoulis, Armin Iske, Jeremy Levesley
Place of Publication	Heidelberg
Publisher	Springer-Verlag
Pages	27-45
Number of pages	19
Volume	3
Edition	1
ISBN (Print)	9783642168758
DOIs	https://doi.org/10.1007/978-3-642-16876-5_2
Publication status	Published - 2011
Event	6th International Conference on Algorithms for Approximation - Ambleside, United Kingdom Duration: 31 Aug 2009 → 4 Sept 2009

Conference

Conference	6th International Conference on Algorithms for Approximation
Country/Territory	United Kingdom
City	Ambleside
Period	31/08/09 → 4/09/09

Keywords

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

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10.1007/978-3-642-16876-5_2

10preprint2010Submitted manuscript, 201 KB

Cite this

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title = "Algorithms and error bounds for multivariate piecewise constant approximation",

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.",

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author = "Oleg Davydov",

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language = "English",

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booktitle = "Approximation Algorithms for Complex Systems",

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note = "6th International Conference on Algorithms for Approximation ; Conference date: 31-08-2009 Through 04-09-2009",

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Davydov, O 2011, Algorithms and error bounds for multivariate piecewise constant approximation. in EH Georgoulis, A Iske & J Levesley (eds), Approximation Algorithms for Complex Systems: Springer Proceedings in Mathematics 2011. 1 edn, vol. 3, Springer-Verlag, Heidelberg, pp. 27-45, 6th International Conference on Algorithms for Approximation, Ambleside, United Kingdom, 31/08/09. https://doi.org/10.1007/978-3-642-16876-5_2

Algorithms and error bounds for multivariate piecewise constant approximation. / Davydov, Oleg.
Approximation Algorithms for Complex Systems: Springer Proceedings in Mathematics 2011. ed. / Emmanuil H Georgoulis; Armin Iske; Jeremy Levesley. Vol. 3 1. ed. Heidelberg: Springer-Verlag, 2011. p. 27-45.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution book

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T1 - Algorithms and error bounds for multivariate piecewise constant approximation

AU - Davydov, Oleg

PY - 2011

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N2 - 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.

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KW - variables

KW - piecewise constants

KW - algorithms

KW - Sobolev-Poincaré inequalities

KW - Haar wavelets

KW - tree approximation

U2 - 10.1007/978-3-642-16876-5_2

DO - 10.1007/978-3-642-16876-5_2

M3 - Conference contribution book

SN - 9783642168758

VL - 3

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EP - 45

BT - Approximation Algorithms for Complex Systems

A2 - Georgoulis, Emmanuil H

A2 - Iske, Armin

A2 - Levesley, Jeremy

PB - Springer-Verlag

CY - Heidelberg

T2 - 6th International Conference on Algorithms for Approximation

Y2 - 31 August 2009 through 4 September 2009

ER -

Algorithms and error bounds for multivariate piecewise constant approximation

Abstract

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Keywords

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