Adaptive SOR methods based on the Wolfe conditions
It offers a practical adaptive parameter selection for SOR methods, reducing the need for costly estimation in solving linear systems.
The paper introduces adaptive SOR methods that use Wolfe conditions to control the relaxation parameter without extra matrix-vector products, showing favorable numerical performance on symmetric positive definite linear systems.
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.