Jacobi‐Davidson, Gauss‐Seidel and Successive Over‐Relaxation for Solving Systems of Linear Equations

Authors

  • Fatini Dalili Mohammed Department of Computer Sciences and Mathematics, Universiti Teknologi MARA (UiTM) Terengganu, Campus Kuala Terengganu, Malaysia
  • Mohd Rivaie Department of Computer Sciences and Mathematics, Universiti Teknologi MARA (UiTM) Terengganu, Campus Kuala Terengganu, Malaysia

Abstract

Linear systems are applied in many applications such as calculating variables, rates, budgets, making a prediction and others. Generally, there are two techniques of solving system of linear equation including direct methods and iterative methods. Some basic solution methods 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. 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. The comparative results analysis of the three methods is considered. These three methods are compared based on number of iterations, CPU time and error. The numerical results show that Gauss‐Seidel method and SOR method with ω=1.25 are more efficient than others. This research allows researcher to appreciate the use of iterative techniques for solving systems of linear equations that is widely used in industrial applications.

Keywords:

system of linear equation, iterative method, Jacobi‐Davidson, Gauss‐Seidel, Successive Over‐Relaxation

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Published

2017-12-31

How to Cite

Fatini Dalili Mohammed, & Mohd Rivaie. (2017). Jacobi‐Davidson, Gauss‐Seidel and Successive Over‐Relaxation for Solving Systems of Linear Equations. Applied Mathematics and Computational Intelligence (AMCI), 6, 41–52. Retrieved from https://ejournal.unimap.edu.my/index.php/amci/article/view/32

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