Davydov, O. (2012) *Approximation by piecewise constants on convex partitions.* Journal of Approximation Theory, 164 (2). pp. 346-352. ISSN 0021-9045

Official URL: http://dx.doi.org/10.1016/j.jat.2011.11.001

## Abstract

We show that the saturation order of piecewise constant approximation in Lp norm on convex partitions with N cells is N−2/(d+1), where d is the number of variables. This order is achieved for any on a partition obtained by a simple algorithm involving an anisotropic subdivision of a uniform partition. This improves considerably the approximation order N−1/d achievable on isotropic partitions. In addition we show that the saturation order of piecewise linear approximation on convex partitions is N−2/d, the same as on isotropic partitions.

Item type: | Article |
---|---|

ID code: | 40283 |

Keywords: | approximation, convex partitions , mathematical analysis, isotropic partitions, Probabilities. Mathematical statistics, Analysis, Applied Mathematics, Mathematics(all), Numerical Analysis |

Subjects: | Science > Mathematics > Probabilities. Mathematical statistics |

Department: | Faculty of Science > Mathematics and Statistics |

Related URLs: | |

Depositing user: | Pure Administrator |

Date Deposited: | 02 Jul 2012 10:16 |

Last modified: | 27 Mar 2014 10:14 |

URI: | http://strathprints.strath.ac.uk/id/eprint/40283 |

### Actions (login required)

View Item |