Sinkhorn limits in finitely many steps

11/29/2019

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by   Alex Cohen, et al.

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Applied to a nonnegative m× n matrix with a nonzero σ-diagonal, the sequence of matrices constructed by alternate row and column scaling conveges to a doubly stochastic matrix. It is proved that if this sequence converges after only a finite number of scalings, then it converges after at most two scalings.