Pisarenko proposed a method for decomposing a random stationary process into a sum of harmonics in white noise. The numerical determination of the frequencies consists of several parts, one of which is the computation of the zeros of a polynomial which is known to vanish on the unit circle only. We describe how this part of the computations can be formulated as an eigenvalue problem for an orthogonal matrix. Several algorithms for such eigenproblems are reviewed, one of which enables highly parallel computations.