Optimal covering points and curves

Justin Tzou, Brian Wetton*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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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.
Original languageEnglish
Pages (from-to)1796-1804
Number of pages9
JournalAIMS Mathematics
Volume4
Issue number6
DOIs
Publication statusPublished - 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

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