Do you know where I can find an 'elegant' proof of convergence of the Sinkhorn Knopp algorithm?
The original paper by Sinkhorn and Knopp contains a costructive proof which is elementary but too intricate.
Other papers I found deal with the rate of convergence of the algorithm but they assume that the algorithm converges (obviously for a certain class of matrices).
Here is a paper with a proof of convergence (see Section 2), based on some simple facts about so-called Kullback-Leibler divergence. Is this elegant enough?
D. Chakrabarty and S. Channa: Better and Simpler Error Analysis of the Sinkhorn-Knopp Algorithm for Matrix Scaling