An Arithmetic Proof of John’s Ellipsoid Theorem
نویسندگان
چکیده
Using an idea of Voronoi in the geometric theory of positive definite quadratic forms, we give a transparent proof of John’s characterization of the unique ellipsoid of maximum volume contained in a convex body. The same idea applies to the ‘hard part’ of a generalization of John’s theorem and shows the difficulties of the corresponding ‘easy part’. MSC 2000. 52A21, 52A27, 46B07.
منابع مشابه
John's Walk
We present an affine-invariant random walk for drawing uniform random samples from a convex body K Ă Rn for which the maximum volume inscribed ellipsoid, known as John’s ellipsoid, may be computed. We consider a polytope P “ x P Rn ˇ̌ Ax ď 1 ( where A P R as a special case. Our algorithm makes steps using uniform sampling from the John’s ellipsoid of the symmetrization of K at the current point....
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