Geodesic
Circumscribing an Ellipsoid about the Intersection of Two Ellipsoids
Canadian mathematical bulletin, Tome 11 (1968) no. 3, pp. 437-441

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An ellipsoid G is associated uniquely with a positive definite matrix A via Note that all ellipsoids discussed here are centred at 0. Given G1, and G2 we seek another ellipsoid circumscribed about G1 ∩ G2. It is easy to see that if and only if x'hx ≤ maxi x'aix for all vectors x. 
Kahan, W. Circumscribing an Ellipsoid about the Intersection of Two Ellipsoids. Canadian mathematical bulletin, Tome 11 (1968) no. 3, pp. 437-441. doi: 10.4153/CMB-1968-050-2
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     title = {Circumscribing an {Ellipsoid} about the {Intersection} of {Two} {Ellipsoids}},
     journal = {Canadian mathematical bulletin},
     pages = {437--441},
     year = {1968},
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     doi = {10.4153/CMB-1968-050-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1968-050-2/}
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