Noonan, Jack and Zhigljavsky, Anatoly ORCID: https://orcid.org/0000-0003-0630-8279 2022. Efficient quantisation and weak covering of high dimensional cubes. Discrete and Computational Geometry 68 , pp. 540-565. 10.1007/s00454-022-00396-7 |
Preview |
PDF
- Published Version
Available under License Creative Commons Attribution. Download (1MB) | Preview |
Abstract
Let Zn={Z1,…,Zn} be a design; that is, a collection of n points Zj∈[−1,1]d. We study the quality of quantisation of [−1,1]d by the points of Zn and the problem of quality of coverage of [−1,1]d by Bd(Zn,r), the union of balls centred at Zj∈Zn. We concentrate on the cases where the dimension d is not small, d≥5, and n is not too large, n≤2d. We define the design Dn,δ as a 2d−1 design defined on vertices of the cube [−δ,δ]d, 0≤δ≤1. For this design, we derive a closed-form expression for the quantisation error and very accurate approximations for the coverage area vol([−1,1]d∩Bd(Zn,r)). We provide results of a large-scale numerical investigation confirming the accuracy of the developed approximations and the efficiency of the designs Dn,δ.
Item Type: | Article |
---|---|
Date Type: | Publication |
Status: | Published |
Schools: | Mathematics |
Publisher: | Springer Verlag (Germany) |
ISSN: | 0179-5376 |
Funders: | EPSRC |
Date of First Compliant Deposit: | 14 April 2022 |
Date of Acceptance: | 2 February 2022 |
Last Modified: | 22 May 2023 21:38 |
URI: | https://orca.cardiff.ac.uk/id/eprint/149197 |
Citation Data
Cited 1 time in Scopus. View in Scopus. Powered By Scopus® Data
Actions (repository staff only)
Edit Item |