eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Dagstuhl Seminar Proceedings
1862-4405
2007-06-28
1
18
10.4230/DagSemProc.07071.4
article
A Fast Algorithm for Matrix Balancing
Knight, Philip A.
Ruiz, Daniel
As long as a square nonnegative matrix A contains sufficient nonzero elements, then the matrix can be balanced, that is we can find a diagonal scaling of A that is doubly stochastic. A number of algorithms have been proposed to achieve the balancing, the most well known of these being the Sinkhorn-Knopp algorithm. In this paper we derive new algorithms based on inner-outer iteration
schemes. We show that the Sinkhorn-Knopp algorithm belongs to this family, but other members can converge much more quickly. In particular, we show that while stationary iterative methods offer little or no improvement in many cases, a scheme using a preconditioned conjugate gradient method as the inner
iteration can give quadratic convergence at low cost.
https://drops.dagstuhl.de/storage/16dagstuhl-seminar-proceedings/dsp-vol07071/DagSemProc.07071.4/DagSemProc.07071.4.pdf
Matrix balancing
Sinkhorn-Knopp algorithm
doubly stochastic matrix
conjugate gradient iteration