Numerical computation of some iterative techniques for solving system of linear equations of multivariable

Abstract

In this paper we introduce, numerical computation of some iterative techniques for solving system of linear simultaneous equations of 4 or more variables. Many iterative techniques is presented by the different formulae. Using Jacobi method, Seidel method and SOR method and their results are compared. The software, Matlab 2009a was used to find the solution of the linear simultaneous equations having diagonally dominant in coefficient matrix. Numerical rate of convergence of solution has been found in each calculation. It was observed that the Seidel method converges at the 12iteration while Jacobi and SOR methods converge to the exact value of X(x, y, z, t) with error level of accuracy 〖10〗^(-15) at the 22th iteration respectively. However, when we compare performance, we must compare both cost, speed of convergence. Some numerical examples are given to illustrate the efficiency and robustness of the techniques. It was then concluded that Seidel is the most effective technique.