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Accelerating the Sinkhorn–Knopp iteration by Arnoldi-type methods
Calcolo ( IF 1.7 ) Pub Date : 2020-02-10 , DOI: 10.1007/s10092-020-0359-7
A. Aristodemo , L. Gemignani

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.

中文翻译:

用Arnoldi型方法加速Sinkhorn-Knopp迭代

结果表明,利用正对角线矩阵平衡非负矩阵的问题可以重现为具有特征向量非线性的非线性特征值问题。基于该等效公式,提出了幂方法和Arnoldi过程的一些改编,以计算定义对角变换结构的主导特征向量。数值结果表明,在聚类主导特征值的情况下,我们的新方法极大地加速了传统Sinkhorn-Knopp迭代的收敛,以实现矩阵平衡。
更新日期:2020-02-10
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