### Abstract

Language | English |
---|---|

Pages | 346-352 |

Number of pages | 7 |

Journal | Journal of Approximation Theory |

Volume | 164 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2012 |

### Fingerprint

### Keywords

- approximation
- convex partitions
- mathematical analysis
- isotropic partitions

### Cite this

*Journal of Approximation Theory*,

*164*(2), 346-352. https://doi.org/10.1016/j.jat.2011.11.001

}

*Journal of Approximation Theory*, vol. 164, no. 2, pp. 346-352. https://doi.org/10.1016/j.jat.2011.11.001

**Approximation by piecewise constants on convex partitions.** / Davydov, O.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Approximation by piecewise constants on convex partitions

AU - Davydov, O.

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

KW - approximation

KW - convex partitions

KW - mathematical analysis

KW - isotropic partitions

UR - http://www.scopus.com/inward/record.url?scp=84155165358&partnerID=8YFLogxK

U2 - 10.1016/j.jat.2011.11.001

DO - 10.1016/j.jat.2011.11.001

M3 - Article

VL - 164

SP - 346

EP - 352

JO - Journal of Approximation Theory

T2 - Journal of Approximation Theory

JF - Journal of Approximation Theory

SN - 0021-9045

IS - 2

ER -