منابع مشابه
Convergence Rate of Riemannian Hamiltonian Monte Carlo and Faster Polytope Volume Computation
We give the first rigorous proof of the convergence of Riemannian Hamiltonian Monte Carlo, a general (and practical) method for sampling Gibbs distributions. Our analysis shows that the rate of convergence is bounded in terms of natural smoothness parameters of an associated Riemannian manifold. We then apply the method with the manifold defined by the log barrier function to the problems of (1...
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Let n ≥ 2 be an integer and consider the set Tn of n× n permutation matrices π for which πij = 0 for j ≥ i+ 2. In this paper we study the convex hull of Tn, which we denote by Pn. Pn is a polytope of dimension ( n 2 ) . Our main purpose is to provide evidence for the following conjecture concerning its volume. Let vn denote the minimum volume of a simplex with vertices in the affine lattice spa...
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Let m,n ≥ 1 be integers. Define Tm,n to be the transportation polytope consisting of the m × n non-negative real matrices whose rows each sum to 1 and whose columns each sum to m/n. The special case Bn = Tn,n is the much-studied Birkhoffvon Neumann polytope of doubly-stochastic matrices. Using a recent asymptotic enumeration of non-negative integer matrices (Canfield and McKay, 2007), we determ...
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For a d-dimensional convex lattice polytope P , a formula for the boundary volume vol(∂P ) is derived in terms of the number of boundary lattice points on the first bd/2c dilations of P . As an application we give a necessary and sufficient condition for a polytope to be reflexive, and derive formulae for the f -vector of a smooth polytope in dimensions 3, 4, and 5. We also give applications to...
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The problem of approximating convex bodies by polytopes is an important and well studied problem. Given a convex body K in R, the objective is to minimize the number of vertices (alternatively, the number of facets) of an approximating polytope for a given Hausdorff error ε. Results to date have been of two types. The first type assumes that K is smooth, and bounds hold in the limit as ε tends ...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1991
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-1991-1079024-2