Alternate Minimization and Doubly Stochastic Matrices
Alternate Minimization and Doubly Stochastic Matrices
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
- Department of Mathematics
- Lehman College United States
- Lehman College
Random matrices (algebraic aspects), Mathematics - Number Theory, doubly stochastic matrix, FOS: Mathematics, 11C20, 11B75, 11B99, Mathematics - Combinatorics, minimization, Combinatorics (math.CO), Number Theory (math.NT)
Random matrices (algebraic aspects), Mathematics - Number Theory, doubly stochastic matrix, FOS: Mathematics, 11C20, 11B75, 11B99, Mathematics - Combinatorics, minimization, Combinatorics (math.CO), Number Theory (math.NT)
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