  In this paper a family of fixed point algorithms, generalizing the \PM
method, is considered. A previous work studied the convergence of the methods.
Presented here is a second part of the analysis, concerning the introduction of
some acceleration techniques into the iterative procedures. The purpose of the
research is two-fold: one is improving the performance of the methods in case
of convergence and the second one is widening their application when generating
traveling waves in nonlinear dispersive wave equations, transforming some
divergent into convergent cases. Two families of acceleration techniques are
considered: the vector extrapolation methods and the Anderson acceleration
methods. A comparative study through several numerical experiments is carried
out.
