A new SOR-type iteration method for solving linear systems

Abstract

Many discretization methods for continuous dynamical systems have the iterative nature and therefore can provide iterative techniques for solving problems in numerical linear algebra. In this paper, based on the discrete gradient and the variation-of-constants formula for ordinary differential equations, a new SOR-type iteration method is proposed for solving the linear system Ax=b. The convergence of the new method is guaranteed by the decay of the Liapunov function. Numerical experiments are carried out to show the effectiveness of the new method.