Solving large systems of linear equations using iterative methods (Jacobi-Davidson, Gauss-Seidel and Successive Over-Relaxation) / Fatini Dalili Mohammed

Generally, there are two techniques of solving system of linear equation including direct methods and iterative methods. Some basic solution methods those known as direct methods are ineffective in solving many equations in large systems due to slower computation. Due to inability of direct methods, iterative methods are practical to be used in large systems of linear equations as they do not need much storage. The comparative results analysis of the three methods is considered. In this project, three indirect methods are used to solve large system of linear equations. The methods are Jacobi Davidson, Gauss-Seidel and Successive Over-Relaxation (SOR) which are well known in the field of numerical analysis. These three methods are compared based on number of iterations and CPU time. The numerical results show that Gauss- SOR method with co=l .25 is more efficient than others. This research will enable us to appreciate the use of iterative techniques for solving systems of linear equations that widely used in industrial applications.