COMPARISON RESULTS ON THE PRECONDITIONED MIXED-TYPE SPLITTING ITERATIVE METHOD FOR M-MATRIX LINEAR SYSTEMS

Consider the linear system Ax = b where the coefficient matrix A is an M-matrix. Here, it is proved that the rate of convergence of the Gauss-Seidel method is faster than the mixed-type splitting and AOR (SOR) iterative methods for solving M-matrix linear systems. Furthermore, we improve the rate of convergence of the mixed-type splitting iterative method by applying a preconditioned matrix. Comparison theorems show that the rate of convergence of the preconditioned Gauss-Seidel method is faster than the preconditioned mixed-type splitting and AOR (SOR) iterative methods. Finally, some numerical examples are presented to illustrate the reality of our results.