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.
Highlights
Solving system of linear simultaneous equations is one of the most important and challenging problems in science and engineering applications
In this paper we introduce, numerical computation of some iterative techniques for solving system of linear simultaneous equations of 4 or more variables
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
Summary
Solving system of linear simultaneous equations is one of the most important and challenging problems in science and engineering applications. Iterative solver is an algorithm [1] that can be used to determine the solutions of a system of linear equations to find the rank of a matrix [3,4,5], and to calculate the inverse of an invertible square matrix. Another point of view, which turns out to be very useful to analyze the algorithm. A sufficient condition for the convergence of Jacobi and Gauss-Seidel methods is that the matrix A of linear system Ax=b is strictly diagonally dominant [6] Theorem.2.3. For any arbitrary matrix A, the necessary condition for the convergence of relaxation method is 0 < w < 2. [9]
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