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On the Complexity of Mixed Discriminants and Related Problems

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Book cover Mathematical Foundations of Computer Science 2005 (MFCS 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3618))

Abstract

We prove that it is #P-hard to compute the mixed discriminant of rank 2 positive semidefinite matrices. We present poly-time algorithms to approximate the ”beast”. We also prove NP-hardness of two problems related to mixed discriminants of rank 2 positive semidefinite matrices. One of them, the so called Full Rank Avoidance problem, had been conjectured to be NP-Complete in [23] and in [25]. We also present a deterministic poly-time algorithm computing the mixed discriminant D(A 1,..,A N ) provided that the linear (matrix) subspace generated by {A 1,..,A N } is small and discuss randomized algorithms approximating mixed discriminants within absolute error.

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Author information

Authors and Affiliations

  1. Los Alamos National Laboratory, Los Alamos, NM, 87545, USA

    Leonid Gurvits

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  1. Leonid Gurvits
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Editor information

Editors and Affiliations

  1. Institute of Mathematics, Gdansk University, Wita Stwosza 57, 80 952, Gdansk, Poland

    Joanna Jȩdrzejowicz  & Andrzej Szepietowski  & 

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Gurvits, L. (2005). On the Complexity of Mixed Discriminants and Related Problems. In: Jȩdrzejowicz, J., Szepietowski, A. (eds) Mathematical Foundations of Computer Science 2005. MFCS 2005. Lecture Notes in Computer Science, vol 3618. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11549345_39

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  • DOI: https://doi.org/10.1007/11549345_39

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-28702-5

  • Online ISBN: 978-3-540-31867-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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