Permanents, $$\alpha $$ α -permanents and Sinkhorn balancing

Francis Sullivan () and Isabel Beichl ()

Computational Statistics, 2014, vol. 29, issue 6, 1793-1798

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 $$\alpha $$ α -permanents of some previously studied matrices. Copyright Springer-Verlag Berlin Heidelberg (outside the USA) 2014

Keywords: Matrix scaling; Doubly stochastic matrix; Sequential importance sampling (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s00180-014-0506-1

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