  We consider the entropic regularization of discretized optimal transport and
propose to solve its optimality conditions via a logarithmic Newton iteration.
We show a quadratic convergence rate and validate numerically that the method
compares favorably with the more commonly used Sinkhorn--Knopp algorithm for
small regularization strength. We further investigate numerically the
robustness of the proposed method with respect to parameters such as the mesh
size of the discretization.
