ENHANCING THE CONVERGENCE RATE OF A PRECONDITIONED ACCELERATED OVERRELAXATION METHOD FOR LARGE SPARSE LINEAR ALGEBRAIC SYSTEMS VIA A THIRD-LEVEL REFINEMENT STRATEGY

Abstract

The accelerated overrelaxation (AOR) method is a widely used iterative method for solving large, sparse systems of linear equations due to its simplicity and low memory requirements. However, the AOR method may not always converge or may converge slowly for certain type of matrices. Preconditioning and refinement strategies are some of the techniques that have been introduced to overcome these limitations. This study presents the third refinement of a preconditioned accelerated overrelaxation iterative method, geared towards further enhancement of its convergence properties. It involves the application of a repeated refinement technique to a preconditioned AOR method to minimize its spectral radius, thereby reducing the iteration count and computational time. Theoretical convergence analysis and numerical experiments confirm the enhanced convergence properties, efficiency and accuracy of the refined method, significantly outperforming the existing AOR, its preconditioned variant and earlier refinements. This enhancement has far-reaching implications for solving large-scale linear systems in varied scientific and engineering application.