Exact primitives for smallest enclosing ellipses

The problem of finding the unique closed ellipsoid of smallest volume enclosing an n-point set P in d-space (known as the Loroner-John ellipsoid of P [5]) is an instance of convex programming and can be solved by general methods in time O(n) if the dimension is tixed [12, 6, 3, 1]. The problernspeciflc parts of these methods are encapsulated in primitiu e operations that deal with subproblems of constant sise. We derive explicit formulae for the primitive operations of Welsl’s randomised method [12] in dimension d = 2. Compared to previous ones [9, 7, 8], these formulae me simpler and faster to evaluate, and they only contain rational expressions, zdlowing for an exact solution.