Abstract
Polynomial acceleration methods from computational optimization can be applied to accelerating MCMC. For example, a geometrically convergent MCMC may be accelerated to be a perfect sampler in special circumstances. An equivalence between Gibbs sampling of Gaussian distributions and classical iterative methods can be established using matrix splittings, allowing direct application of Chebyshev acceleration. The conjugate gradient method can also be adapted to give an accelerated sampler for Gaussian distributions, that is perfect in exact arithmetic.