  In the $GW$ approximation, the screened interaction $W$ is a non-local and
dynamical potential that usually has a complex frequency dependence. A full
description of such dependence is possible but often computationally demanding.
For this reason, it is still common practice to approximate $W(\omega)$ using a
plasmon pole (PP) model. Such approach, however, may deliver an accuracy
limited by its simplistic description of the frequency dependence of the
polarizability, i.e. of $W$.
  In this work we explore a multi-pole approach (MPA) and develop an effective
representation of the frequency dependence of $W$. We show that an appropriate
sampling of the polarizability in the frequency complex plane and a multi-pole
interpolation can lead to a level of accuracy comparable with full-frequency
methods at much lower computational cost. Moreover, both accuracy and cost are
controllable by the number of poles used in MPA. Eventually we validate the MPA
approach in selected prototype systems, showing that full-frequency quality
results can be obtained with a limited number of poles.
