Sinkhorn's algorithm for doubly stochastic matrices and a problem in diophantine approximation

Doubly stochastic matrices are square matrices with all row sums and column sums equal to 1. Sinkhorn described an "alternate minimization" algorithm that transforms every positive square matrix into a doubly stochastic matrix. Applied to matrices with positive integral coordinates, the algorithm suggests a problem in diophantine approximation.

Mel Nathanson