Foundations of Computational Mathematics

, Volume 16, Issue 2, pp 329–342 | Cite as

Computing the Permanent of (Some) Complex Matrices

  • Alexander BarvinokEmail author


We present a deterministic algorithm, which, for any given \(0< \epsilon < 1\) and an \(n \times n\) real or complex matrix \(A=\left( a_{ij}\right) \) such that \(\left| a_{ij}-1 \right| \le 0.19\) for all \(i, j\) computes the permanent of \(A\) within relative error \(\epsilon \) in \(n^{O\left( \ln n -\ln \epsilon \right) }\) time. The method can be extended to computing hafnians and multidimensional permanents.


Permanent Hafnian Algorithm 

Mathematics Subject Classification

15A15 68C25 68W25 



The author is grateful to the anonymous referees for their careful reading of the paper, useful suggestions and interesting questions.


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Copyright information

© SFoCM 2014

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of MichiganAnn ArborUSA

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