A fast algorithm for matrix balancing (Q2841064)
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scientific article; zbMATH DE number 6190573
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A fast algorithm for matrix balancing |
scientific article; zbMATH DE number 6190573 |
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A fast algorithm for matrix balancing (English)
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24 July 2013
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matrix balancing
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Sinkhorn-Knopp algorithm
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doubly stochastic matrix
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conjugate gradient iteration
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sparse matrices
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inexact Newton method
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0.91897005
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0.89480853
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0.88986856
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0.87313867
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0.8694097
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The Sinkhorn-Knopp algorithm [\textit{R. Sinkhorn} and \textit{P. Knopp}, Pac. J. Math. 21, 343--348 (1967; Zbl 0152.01403)] offers an approach to balancing matrices but it does not work well for sparse matrices. In this paper, the authors derive some new algorithms that are fast for large matrix-balancing problems. They show that an inexact Newton method offers a simple way of overcoming the limitation of the Sinkhorn-Knopp algorithm. They make sure that if they remain in the positive cone then they show improvements for both symmetric and nonsymmetric matrices. They point out that if the diagonal of the matrix contain widely varying elements then the proposed algorithm converges slowly.
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