Permanents, alpha-permanents and Sinkhorn balancing
F Sullivan, Isabel M. Beichl
The method of Sinkhorn balancing that starts with a non-negative square matrix and iterates to produce a related doubly stochastic matrix has been used with some success to estimate the values of the permanent in some cases of physical interest, However it is often claimed that Sinkhorn balancing is slow to converge and hence not useful for efficient computation. In this paper we ex[plain how some simple low cost pre-processing allows one to guarantee that Singhorn balancing always converges linearly. We illustrate this approach by efficiently and accurately computing permanents and alpha-permanents of some previously studied matrices.