2018/10/23 by A. Aristodemo, Aristodemo, A., Luca Gemignani +1
Computer Science · Mathematics · #65F15 #Advanced Optimization Algorithms Research #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Statistical and numerical algorithms
paper · pdf · doi:10.48550/arxiv.1810.09700
openalex publication_date 2018/10/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.