A note on computing the intersection of spheres in \(\mathbb{R}^{n}\)
Maioli, Douglas Silva ; Lavor, Carlile Campos ; Gonçalves, Douglas Soares
ANZIAM Journal, Tome 59 (2018), / Harvested from Australian Mathematical Society
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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

Publié le : 2018-01-01
DOI : https://doi.org/10.21914/anziamj.v59i0.11829 
@article{11829,
     title = {A note on computing the intersection of spheres in \(\mathbb{R}^{n}\)},
     journal = {ANZIAM Journal},
     volume = {59},
     year = {2018},
     doi = {10.21914/anziamj.v59i0.11829},
     language = {EN},
     url = {http://dml.mathdoc.fr/item/11829}
}

Maioli, Douglas Silva; Lavor, Carlile Campos; Gonçalves, Douglas Soares. A note on computing the intersection of spheres in \(\mathbb{R}^{n}\). ANZIAM Journal, Tome 59 (2018) . doi : 10.21914/anziamj.v59i0.11829. http://gdmltest.u-ga.fr/item/11829/