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Permanents, \(\alpha \)-permanents and Sinkhorn balancing

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Abstract

The method of Sinkhorn balancing that starts with a non-negative square matrix and iterates to produce a related doubly stochastic matrix has been used with some success to estimate the values of the permanent in some cases of physical interest. However, it is often claimed that Sinkhorn balancing is slow to converge and hence not useful for efficient computation. In this paper, we explain how some simple, low cost pre-processing allows one to guarantee that Sinkhorn balancing always converges linearly. We illustrate this approach by efficiently and accurately computing permanents and \(\alpha \)-permanents of some previously studied matrices.

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  1. Certain commercial equipment, instruments, or materials are identified in this paper to foster understanding. Such identification does not imply recommendation or endorsement by the National Institute of Standards and Technology, nor does it imply that the materials or equipment identified are necessarily the best available for the purpose.

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Authors and Affiliations

  1. IDA/CCS, 17100 Science Drive, Bowie, MD , 20715, USA

    Francis Sullivan

  2. NIST, 100 Bureau Drive, Gaithersburg, MD , 20899, USA

    Isabel Beichl

Authors
  1. Francis Sullivan
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  2. Isabel Beichl
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Correspondence to Isabel Beichl.

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Sullivan, F., Beichl, I. Permanents, \(\alpha \)-permanents and Sinkhorn balancing. Comput Stat 29, 1793–1798 (2014). https://doi.org/10.1007/s00180-014-0506-1

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  • DOI: https://doi.org/10.1007/s00180-014-0506-1

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