In this paper, a new method to determine the rate of Convergence of some terative methods for solving the systems of linear algebraic equations is proposed. The method is simpler and more effective than previons methods.It can show how the rate of convergence depends on some elements of the coefficient matrix of the system.Several iterative methods are considers and numerical results are given to illustrate our method and conclusions.

In this paper,we analyse the rate of convergence of some precontditionedonjugate gradient methods,namely ICCG method ILUCG(k) method, ILUCG (p)method and so called "TCG method" with a number of splittings for preconditioning the coefficient matrix A of the system of linear algebraic equation to be solved under the condition that A is diagonally dominant. Several numeriical examples are given to illustrate our analysis.