  Because the expense of estimating the optimal value of the relaxation
parameter in the successive over-relaxation (SOR) method is usually
prohibitive, the parameter is often adaptively controlled. In this paper, new
adaptive SOR methods are presented that are applicable to a variety of
symmetric positive definite linear systems and do not require additional
matrix-vector products when updating the parameter. To this end, we regard the
SOR method as an algorithm for minimising a certain objective function, which
yields an interpretation of the relaxation parameter as the step size following
a certain change of variables. This interpretation enables us to adaptively
control the step size based on some line search techniques, such as the Wolfe
conditions. Numerical examples demonstrate the favourable behaviour of the
proposed methods.
