Alternate minimization and doubly stochastic matrices

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.

16 pages; minor corrections and improvements

References in corpus (1)

• A review of matrix scaling and Sinkhorn's normal form for matrices and positive maps

Cited by in corpus (2)

• Matrix scaling, explicit Sinkhorn limits, and arithmetic
• Matrix scaling and explicit doubly stochastic limits