  We propose a method for the resummation of divergent perturbative expansions
in quantum electrodynamics and related field theories. The method is based on a
nonlinear sequence transformation and uses as input data only the numerical
values of a finite number of perturbative coefficients. The results obtained in
this way are for alternating series superior to those obtained using Pad\'{e}
approximants. The nonlinear sequence transformation fulfills an
accuracy-through-order relation and can be used to predict perturbative
coefficients. In many cases, these predictions are closer to available analytic
results than predictions obtained using the Pad\'{e} method.
