  Scaling algorithms for entropic transport-type problems have become a very
popular numerical method, encompassing Wasserstein barycenters, multi-marginal
problems, gradient flows and unbalanced transport. However, a standard
implementation of the scaling algorithm has several numerical limitations: the
scaling factors diverge and convergence becomes impractically slow as the
entropy regularization approaches zero. Moreover, handling the dense kernel
matrix becomes unfeasible for large problems. To address this, we combine
several modifications: A log-domain stabilized formulation, the well-known
epsilon-scaling heuristic, an adaptive truncation of the kernel and a
coarse-to-fine scheme. This permits the solution of larger problems with
smaller regularization and negligible truncation error. A new convergence
analysis of the Sinkhorn algorithm is developed, working towards a better
understanding of epsilon-scaling. Numerical examples illustrate efficiency and
versatility of the modified algorithm.
