### 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.

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 |
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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 | |

Publication status | Published - 2011 |

Event | 6th International Conference on Algorithms for Approximation - Ambleside, United Kingdom Duration: 31 Aug 2009 → 4 Sep 2009 |

### Conference

Conference | 6th International Conference on Algorithms for Approximation |
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Country | United Kingdom |

City | Ambleside |

Period | 31/08/09 → 4/09/09 |

### Fingerprint

### 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