Alternate minimization and doubly stochastic matrices

Melvyn B. Nathanson

Alternate minimization and doubly stochastic matrices

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arxiv 1812.11930 v3 pith:LFA5HGJI submitted 2018-12-31 math.CO math.NT

Melvyn B. Nathanson This is my paper · ORCID

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keywords convergesmatrixalgorithmapplieddoublyiterationsmatricesminimization

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abstract

Sinkhorn's alternative minimization algorithm applied to a positive $n\times n$ matrix converges to a doubly stochastic matrix. If the algorithm, applied to a $2\times 2$ matrix, converges in a finite number of iterations, then it converges in at most two iterations, and the structure of such matrices is determined.

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Closed Form of a Generalized Sinkhorn Limit
math.GM 2025-05 reject novelty 6.0 of 10

A closed form for the 2x2 generalized Sinkhorn limit is presented, together with an incomplete proof sketch that all generalized Sinkhorn entries are algebraic with bounded degree.

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