Parametric Reaccelerated Overrelaxation (PROR) method for numerical solution of linear systems

Abstract

This paper proposes the Parameterized Reaccelerated Overrelaxation (PROR) method for numerical solution of linear systems arising from the discretization of partial differential equations. The method is a three-parameter generalization of the Reaccelerated overrelaxation (ROR) method. An expression for the eigenvalues of the iteration matrix of the method is obtained in terms of the eigenvalues of the corresponding Jacobi iteration matrix. Functional relations for determining the optimum values of the parameters are established. Numerical examples are presented to validate theoretical results as well as compare with existing methods. Results showed that the method is suitable and compares favourably with AOR, ROR and PAOR methods