The rate of convergence is studied on a cluster of 30 argon atoms where the inter-atomic distance is, on average, less than the half of the argon-argon equilibrium distance. This high-density system allows for the testing the algorithm's robustness under high screening regimes. Figure ?? shows the convergence of the screened frequency-dependent polarizabilities in terms of the logarithm (base 10) of the residual defined in Eq.( ) for a single frequency ν n , as function of the number of iterations in the case of a simple fixed-point solution of Eq.( ) where line 18 in Algorithm 1 is skipped.