Stability and complexity of mixed discriminants
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We show that the mixed discriminant of n positive semidefinite n × n real symmetric matrices can be approximated within a relative error ϵ >0 in quasi-polynomial n^O( n -ϵ) time, provided the distance of each matrix to the identity matrix in the operator norm does not exceed some absolute constant γ_0 >0. We then deduce a similar result for the mixed discriminant of doubly stochastic n-tuples of matrices from the Marcus - Spielman - Srivastava bound on the roots of the mixed characteristic polynomial.
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