Attaining the Optimal Gaussian Diffusion Acceleration

The notion of diffusion via a stochastic process has been used as a means to approximate desired underlying probability distributions. An important task in such an application is to design a drift so as to accelerate the convergence. This problem can be cast as a special type of inverse eigenvalue problem where the inverse of a given covariance matrix is to be perturbed by skew-symmetric matrices so that all resulting eigenvalues have identical real part. As such, this paper describes how the optimal rate of Gaussian diffusion acceleration can be attained both theoretically and numerically.