Improvements of Successive Overrelaxation Iterative (SOR) Method for L-Matrices

Abstract

In order to accelerate the convergence of the classical iterative schemes, such as Jacobi, Gauss-Seidel and SOR, for the solution of the linear system 𝐴𝑥 = 𝑏, several classes of preconditioners have been introduced. The present work proposes a preconditioner of the class 𝐼 + 𝑆 applied to the classical SOR iterative matrix for linear systems with an irreducible L-matrix as the coefficient matrix. Convergence conditions for the preconditioned system are derived and analysed using standard procedures available in literature. Comparison of results for various spectral radii obtained from numerical experiments proved to be in agreement with the theorems advanced.