  In this paper, we present a method for the computation of the low-lying real
eigenvalues of the Wilson-Dirac operator based on the Arnoldi algorithm. These
eigenvalues contain information about several observables. We used them to
calculate the sign of the fermion determinant in one-flavor QCD and the sign of
the Pfaffian in N=1 super Yang-Mills theory. The method is based on polynomial
transformations of the Wilson-Dirac operator, leading to considerable
improvements of the computation of eigenvalues. We introduce an iterative
procedure for the construction of the polynomials and demonstrate the
improvement in the efficiency of the computation. In general, the method can be
applied to operators with a symmetric and bounded eigenspectrum.
