Third Refinement of Parametric Reaccelerated Overrelaxation Iterative Method for Linear Algebraic Systems

Abstract

The solution of large-scale linear algebraic systems of the form , is a critical challenge in scientific computing, with iterative methods playing a pivotal role in addressing these systems efficiently. Building upon prior advancements by Isah et. al., 2022 and Vatti et. al., 2020, this study introduces the Third Refinement of the Parametric Reaccelerated Overrelaxation (TRPROR) method, an iterative scheme that synergizes features of Accelerated Overrelaxation (AOR), Parametric Accelerated Overrelaxation (PAOR), and Reaccelerated Overrelaxation (ROR) methods. The refined method optimizes parameter selection to enhance convergence rates and computational efficiency. The goal in all iterative methods for solving linear systems is to minimize the spectral radius to reduce the number of iterations required for convergence. Numerical examples demonstrated the superior efficiency of the TRPROR method compared to the standard AOR, ROR, PAOR, and PROR method.