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. We consider a polytope \mathcal{P = \{x \in R^n \mid Ax \leq 1\} where A \in R^{m \times n} as a special case.
After 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 = \{x \in R^n \mid Ax \leq 1\} where A \in R^{m \times n} as a special case.