Aitken's acceleration method, or delta-squared process, is used for
accelerating the rate of convergence of a sequence (from linear to
quadratic), here applied to the fixed point iteration scheme of a
function.

References

Quarteroni, A., and F. Saleri (2006). Scientific Computing with Matlab
and Octave. Second Edition, Springer-Verlag, Berlin Heidelberg.

# Find a zero of f(x) = cos(x) - x*exp(x)# as fixpoint of phi(x) = x + (cos(x) - x*exp(x))/2phi <- function(x) x + (cos(x) - x*exp(x))/2aitken(phi, 0) #=> 0.5177574