IMPROVING PRECONDITIONED GAUSS-SEIDEL ITERATIVE METHOD FOR L-MATRICES

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  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  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.