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On the Complexity of Mixed Discriminants and Related Problems

  • Leonid Gurvits
Part of the Lecture Notes in Computer Science book series (LNCS, 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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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Leonid Gurvits
    • 1
  1. 1.Los Alamos National LaboratoryLos AlamosUSA

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