Two Modified Iterative Methods for Solving Linear Systems by M-matrix

Abstract

In the present work, to provide the preconditioning effect on each row of the coefficient matrix of a linear system, we consider a new preconditioner $(I+C+P_2)$ which is formed by combining the preconditioners $(I+C)$ [3] and $(I+P_2)$ [2] and applied to two classical iterative methods namely Jacobi method and Gauss-Seidel method. We provide some comparison theorems and numerical examples to illustrate the efficiency of the two new methods. The comparison theorems and numerical experiments show that both the new methods are better than the respective classical iterative methods and finally the results also show that the new Gauss-Seidel method is faster than the new Jacobi iterative method.