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Accelerating the Sinkhorn-Knopp iteration by Arnoldi-type methods. (English) Zbl 1437.65015
Summary: It is shown that the problem of balancing a nonnegative matrix by positive diagonal matrices can be recast as a nonlinear eigenvalue problem with eigenvector nonlinearity. 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.
MSC:
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
65H17 Numerical solution of nonlinear eigenvalue and eigenvector problems
Software:
JDQR; JDQZ
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