IMPLICATIONS OF CONVERGENCE-RATES IN SINKHORN BALANCING

Let D(N) be the set N X N stochastic matrices without zero columns. St arting with a matrix A(0) is-an-element-of D(N), Sinkhorn balancing is the iteration of alternately normalizing the column and row sums of A (0). It has been shown that if A(0) has total support then the iterati on converges geometrically to a doubly stochastic limit. We show that the converse is true: geometric convergence implies total support.