  It is shown that the problem of balancing a nonnegative matrix by positive
diagonal matrices can be recast as a constrained nonlinear multiparameter
eigenvalue problem. Based on this equivalent formulation some adaptations of
the power method and Arnoldi process are proposed for computing the dominant
eigenvector which defines the structure of the diagonal transformations.
Numerical results illustrate that our novel methods accelerate significantly
the convergence of the customary Sinkhorn-Knopp iteration for matrix balancing
in the case of clustered dominant eigenvalues.
