Preconditioned SOR iterative methods for L-matrices

Abstract

A preconditioner of the type 𝐼+𝑆 for speeding up convergence of the successive overrelaxation (SOR) iterative method for solving linear system 𝐴x=𝑏 is proposed. Two forms of the preconditioned SOR iteration are obtained and implemented, under limited conditions imposed on the coefficient matrix of the original linear system. Convergence properties are analyzed and established in conformity with standard procedures. The rates of convergence of the preconditioned iterations are shown to supersede that of the SOR method. Numerical experiments confirmed the established theoretical results.