A NOTE ON COMPUTING THE INTERSECTION OF SPHERES IN

A NOTE ON COMPUTING THE INTERSECTION OF SPHERES IN

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, b...

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Bibliographic Details
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 Cambridge University Press 01-10-2017
Subjects:
Applied mathematics
Decomposition
Geometry
Spheres
Trilateration
Online Access:Get full text
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Summary: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.
ISSN:1446-1811
1446-8735
DOI:10.1017/S1446181117000372