Second Refinement of Jacobi Iterative Method for Solving Linear System of Equations

Tesfaye Kebede Eneyew (Department of Mathematics, Bahir Dar University)
Gurju Awgichew (Department of Mathematics, Bahir Dar University)
Eshetu Haile (Department of Mathematics, Bahir Dar University)
Gashaye Dessalew Abie (Department of Mathematics, Bahir Dar University)

International Journal of Computing Science and Applied Mathematics-IJCSAM
Vol. 5 No. 2 (2019)

In this paper, the new method called second refinement of Jacobi (SRJ) method for solving linear system of equations is proposed. The method can be used to solve ODE and PDE problems where the problems are reduced to linear system of equations with coefficient matrices which are strictly diagonally dominant (SDD) or symmetric positive definite matrices (SPD) or M-matrices. In this case, our new method minimizes the number of iterations as well as spectral radius and increases rate of convergence. Few numerical examples are considered to show the efficiency of SRJ over Jacobi (J) and refinement of Jacobi (RJ) methods.