A note on computing the intersection of spheres in \(\mathbb{R}^{n}\)

Authors

  • Douglas Silva Maioli Department of Applied Mathematics - IMECC - University of Campinas, Campinas. http://orcid.org/0000-0001-6995-4003
  • Carlile Campos Lavor Department of Applied Mathematics - IMECC - University of Campinas, Campinas.
  • Douglas Soares Gonçalves Department of Mathematics - CCFM - Federal University of Santa Catarina, Florianópolis.

DOI:

https://doi.org/10.21914/anziamj.v59i0.11829

Keywords:

sphere intersection, \(n\)-dimensional spheres, QR decomposition.

Abstract

Finding the intersection of \(n\)-dimensional spheres in \(\mathbb{R}^{n}\) is an interesting problem with applications in trilateration, global positioning systems, multidimensional scaling and distance geometry. In this paper, we generalize some known results on finding the intersection of spheres, based on QR decomposition. Our main result describes the intersection of any number of \(n\)-dimensional spheres without the assumption that the centres of the spheres are affinely independent. A possible application in the interval distance geometry problem is also briefly discussed. doi:10.1017/S1446181117000372

Published

2018-01-03

Issue

Section

Articles for Printed Issues