IMPROVING PRECONDITIONED GAUSS-SEIDEL ITERATIVE METHOD FOR 𝑳 −MATRICES

Abstract

The Gauss-Seidel is a well-known iterative method for solving the linear system 𝐴𝑥 = 𝑏. Convergence of this method is guaranteed for linear systems whose coefficient matrix 𝐴 is strictly or irreducibly diagonally dominant, Hermitian positive definite and invertible 𝐻 −matrix. In this current work, a preconditioned version of the Gauss-Seidel method is used to accelerate the convergence of this iterative method towards the solution of linear system 𝐴𝑥 = 𝑏 under mild conditions imposed on 𝐴. Convergence theorems on preconditioned Gauss-Seidel iterative method are advanced and proved. The superiority of Preconditioned Gauss-Seidel method is demonstrated by solving some numerical examples.