  The limiting distribution of the normalized number of comparisons used by
Quicksort to sort an array of n numbers is known to be the unique fixed point
with zero mean of a certain distributional transformation S. We study the
convergence to the limiting distribution of the sequence of distributions
obtained by iterating the transformation S, beginning with a (nearly) arbitrary
starting distribution. We demonstrate geometrically fast convergence for
various metrics and discuss some implications for numerical calculations of the
limiting Quicksort distribution. Finally, we give companion lower bounds which
show that the convergence is not faster than geometric.
