  We report on some preparatory investigations for the simulation of the QCD
Schroedinger functional with a non-hermitian polynomial hybrid Monte Carlo
algorithm. The complex spectrum of the non-hermitean free operator with SF
boundary condititons is computed semianalytically. Then it is shown how one can
obtain relevant information on the boundary of the spectral domain also in the
presence of nontrivial gaugefields by monitoring the behavior of polynomials in
the Wilson operator applied on random vectors.
