Solving Large System of Linear Equation Using Successive Over‐ Relaxation, Conjugate Gradient and Preconditioned Conjugate Gradient

Authors

  • Nurhanani Abu Bakar Department of Computer Science and Mathematics, MARA University of Technology (UiTM) Terengganu, Campus Kuala Terengganu, Malaysia

Abstract

System of linear equations is widely used especially in industries. Industrial mathematical applications usually involve large problem. System of linear equation can be solved using direct and indirect method. Direct method requires the use of inverse matrix to solve the
problem. However, for large system of linear equation, finding an inverse could be difficult and time consuming. Therefore, indirect methods in the form of numerical calculation such as Successive Over‐Relaxation, Conjugate Gradient and Preconditioned Conjugate
Gradient are used. The aim of this research is to compare the performance of those three methods to solve variety of system of linear equation from small scale to large scale in term of number of iteration and CPU time. Numerical results show that the Conjugate
Gradient method is the best method for solving system of linear equation in terms of both number of iteration and CPU time. Above all, those three methods could be used to solve system of linear equations.

Keywords:

System of linear equation, Iterative method, Successive Over‐Relaxation, Conjugate Gradient, Preconditioned Conjugate Gradient

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Published

2017-12-31

How to Cite

Nurhanani Abu Bakar. (2017). Solving Large System of Linear Equation Using Successive Over‐ Relaxation, Conjugate Gradient and Preconditioned Conjugate Gradient. Applied Mathematics and Computational Intelligence (AMCI), 6, 83–98. Retrieved from https://ejournal.unimap.edu.my/index.php/amci/article/view/189

Issue

Vol. 6 (2017): December (2017)

Section

Articles