Before revision: We present an affine-invariant random walk for drawing uniform random samples from a convex body K \subset R^n for which the maximum volume inscribed ellipsoid , known as John's ellipsoid, may be computed.
After revision: We present an affine-invariant random walk for drawing uniform random samples from a convex body K \subset R^n that uses maximum volume inscribed ellipsoid , known as John's ellipsoid, may be computed.