A NOTE ON COMPUTING THE INTERSECTION OF SPHERES IN $\mathbb{R}^{n}

• Published in: The ANZIAM journal Vol. 59; no. 2; pp. 271 - 279
• Main Authors: MAIOLI, D. S., LAVOR, C., GONÇALVES, D. S.
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 01-10-2017
• Subjects: secondary 15A03; primary 51K05; QR decomposition; n-dimensional spheres; sphere intersection
• ISSN: 1446-1811; 1446-8735
• DOI: 10.1017/S1446181117000372

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.