Abstract
We consider the optimal covering of the unit square by N circles. By optimal, we mean the covering that can be done with N circles of minimum radius. Equivalently, we study the problem of the optimal placement of N points such that the maximum over all locations in the square of the distance of the location to the set of points is minimized. We propose a new algorithm that can identify optimal coverings to high precision. Numerical predictions of optimal coverings for N = 1 to 16 agree with
the best known results in the literature. We use the optimal designs in approximations to two novel, related problems involving the optimal placement of curves.
the best known results in the literature. We use the optimal designs in approximations to two novel, related problems involving the optimal placement of curves.
| Original language | English |
|---|---|
| Pages (from-to) | 1796-1804 |
| Number of pages | 9 |
| Journal | AIMS Mathematics |
| Volume | 4 |
| Issue number | 6 |
| DOIs | |
| Publication status | Published - 2019 |
Bibliographical note
Copyright the Author(s) 2019. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.Keywords
- covering
- regularized Newton method
- experimental design
- optimal networks
- fuel cell channels