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

Douglas Silva Maioli, Carlile Campos Lavor, Douglas Soares Gonçalves

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

Keywords


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



DOI: http://dx.doi.org/10.21914/anziamj.v59i0.11829



Remember, for most actions you have to record/upload into this online system
and then inform the editor/author via clicking on an email icon or Completion button.
ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.