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 G 1 , and G 2 we seek another ellipsoid circumscribed about G 1 ∩ G 2 . It is easy to see that if and only if x'hx ≤ max i x'a i x for all vectors x.