We present a simple randomized polynomial time algorithm to approximate the
mixed discriminant of n positive semidefinite n×n matrices within a
factor 2O(n). Consequently, the algorithm allows us to approximate in
randomized polynomial time the permanent of a given n×n non-negative
matrix within a factor 2O(n). When applied to approximating the permanent,
the algorithm turns out to be a simple modification of the well-known
Godsil-Gutman estimator