The SOR iterative method is commonly used for the solution of large,
sparse linear systems that arise in conjunction with the approximation
to partial differential equations. Its rate of convergence is dependent
on the value chosen for the iteration parameter $\omega$. Following
Young \cite{kn:Young81}, the number of iterations required for
convergence is minimal when this parameter has an optimal value,
$\omega_{b}$, which minimizes the spectral radius of the SOR iteration
matrix.  Determination of this parameter, however, is difficult in most
cases but may be determined adaptively at the expense of some
computational work \cite{kn:Kincaid79}.

In this paper we investigate three different acceleration techniques
applied to SOR through the solution of a variety of linear systems. The
first is that proposed by Dancis \cite{kn:Dancis91} where a value of
$\omega$ is chosen based on a polynomial acceleration together with a
sub-optimal $\omega<\omega_{b}$. We show that its technique is
extremely sensitive on the value chosen for $\omega$ and that finding
such a value for which acceleration of SOR is attained is as difficult
as determining $\omega_{b}$ itself.

The two other techniques discussed are vector accelerations. We
consider the $\epsilon$ algorithm proposed by Wynn \cite{kn:Wynn62} and
a generalization of Aitken's $\Delta^{2}$ algorithm, proposed by
Graves-Morris \cite{kn:Graves-Morris92}. The experimental results
obtained show that acceleration with respect to SOR is always obtained
with both techniques and that they are not as sensitive to the value
chosen for $\omega$.