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  5. Jacobi‐Davidson, Gauss‐Seidel and Successive Over‐Relaxation for solving systems of linear equations
 
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Jacobi‐Davidson, Gauss‐Seidel and Successive Over‐Relaxation for solving systems of linear equations

Journal
Applied Mathematics and Computational Intelligence (AMCI)
ISSN
2289-1315
Date Issued
2017-12
Handle (URI)
https://amci.unimap.edu.my/
https://ejournal.unimap.edu.my/index.php/amci/article/view/32/22
https://hdl.handle.net/20.500.14170/1493
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 iterativ emethods. Some basic solution methods known as direct methods are ineffective in solving man yequations in large systems duet os lower computation. Due to inability of direct methods, iterative methods are practical to be used in large systems of linear equations ast hey do not need much storage. In this project, three indirect methods are used to solve largesy stem ofline are quations.The methods are JacobiDavidson, Gauss‐Seideland SuccessiveOver‐Relaxation(SOR) which are well known in the field of numerical analysis.The comparativere sults analysis of the three methods is considered.These three methods are compared based on number of iterations, CPU time an error. The numerical results show that Gauss‐Seidel method and SOR met hod with ω=1.25 are more efficient than others. This research allows researcher to appreciatet he use of iterativete chniques for solving systems of linear equations that is widely used in idustrial applications.
Subjects
  • System of linear equa...

  • Iterative method

  • Gauss‐Seidel

  • Successive Over‐Relax...

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Jacobi‐Davidson,Gauss‐Seidel.pdf (204.71 KB)
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Nov 19, 2024
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