Circumscribing an Ellipsoid about the Intersection of Two Ellipsoids

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.