It is well known that Sinkhorn's algorithm converges to a doubly stochastic matrix given a non-negative square input matrix. Knowing that Sinkhorn's algorithm always produces a DSM, I am interested in the opposite: Can every possible DSM be produced with Sinkhorn's algorithm? So can it reach any point on the Birkhoff polytope? I suspect the extreme points (permutation matrices) cannot be reached but is there anything else we can say?
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1arent dsm's fixed points of the algo? – user619894 Sep 13 '24 at 20:03