Methods for scaling to doubly stochastic form

AbstractNew methods for scaling square, nonnegative matrices to doubly stochastic form are described. A generalized version of the convergence theorem of Sinkhorn and Knopp (1967) is proved and applied to show convergence for these new methods. Tests indicate that one of the new methods has significantly better average and worst-case behavior than the Sinkhorn-Knopp method; for one of the 3 × 3 examples of Marshall and Olkin (1968), SK requires 130 times as many operations as the new algorithm to achieve row and column sums 1±10-5