### SECOND REFINEMENT OF GENERALIZED JACOBI ITERATIVE METHOD FOR SOLVING LINEAR SYSTEM OF EQUATIONS

T. K. ENYEW, G. AWGICHEW,, H. HAILE, G. D. ABIE

#### Abstract

The Jacobi and Gauss-Seidel algorithms are among the stationary iterative methods for solving linear system of equations. In this paper, we present the new method which is called secondrefinement of generalized Jacobi (SRGJ) method for solving linear system of equations. This new method is the fastest method to converge to the exact solution as compared with Jacobi (J), refinement of Jacobi (RJ), generalized of Jacobi and refinement of generalized Jacobi (RGJ) method by considering strictly diagonally dominant (SDD), symmetric positive definite (SPD) and M-matrices. It is verified by checking the number of iterations and rate of convergence. The SRGJ method can be applied to solve ODE and PDE problems when finite difference method results system of linear equations with its coefficient matrices are strictly diagonally dominant (SDD) or symmetric positive definite matrices (SPD) or M-matrices.

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