A comparison of the Jacobi method, Successive Over-Relaxation (SOR), Conjugate Gradient (CG), and Preconditioned Conjugate Gradient (PCG) in solving linear systems / Allisya Farhana Azmi Hisham

Four iterative approaches to solve a system of linear equations are considered in this study. The four iteratives approach are Jacobi method, Successive Over Relaxation Method Conjugate Gradient and Preconditioned Conjugate Gradient. This study used symmetric matrices of various sizes, including 3x3...

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Main Author:	Azmi Hisham, Allisya Farhana
Format:	Thesis
Language:	English
Published:	2023
Subjects:	Analytical methods used in the solution of physical problems
Online Access:	https://ir.uitm.edu.my/id/eprint/96627/1/96627.pdf
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id	my-uitm-ir.96627
record_format	uketd_dc
spelling	my-uitm-ir.966272024-06-10T07:21:35Z A comparison of the Jacobi method, Successive Over-Relaxation (SOR), Conjugate Gradient (CG), and Preconditioned Conjugate Gradient (PCG) in solving linear systems / Allisya Farhana Azmi Hisham 2023 Azmi Hisham, Allisya Farhana Analytical methods used in the solution of physical problems Four iterative approaches to solve a system of linear equations are considered in this study. The four iteratives approach are Jacobi method, Successive Over Relaxation Method Conjugate Gradient and Preconditioned Conjugate Gradient. This study used symmetric matrices of various sizes, including 3x3, 4x4, and 6x6 matrices. The outcome demonstrates that, out of all the methods, Preconditioned Conjugate Gradient performs the best. When conducting the investigation, a stopping criterion with a tolerance of e~6 was required. The maximum iteration represents the solution once the calculation has attained the required tolerance. The procedure is more effective it has the smallest iteration. This study makes it possible for researchers or analysts to learn how iterative approaches can be used to comprehend the system solution of linear equations. 2023 Thesis https://ir.uitm.edu.my/id/eprint/96627/ https://ir.uitm.edu.my/id/eprint/96627/1/96627.pdf text en public degree Universiti Teknologi MARA, Terengganu College of Computing, Informatics and Mathematics Jaafar, Ruhana
institution	Universiti Teknologi MARA
collection	UiTM Institutional Repository
language	English
advisor	Jaafar, Ruhana
topic	Analytical methods used in the solution of physical problems
spellingShingle	Analytical methods used in the solution of physical problems Azmi Hisham, Allisya Farhana A comparison of the Jacobi method, Successive Over-Relaxation (SOR), Conjugate Gradient (CG), and Preconditioned Conjugate Gradient (PCG) in solving linear systems / Allisya Farhana Azmi Hisham
description	Four iterative approaches to solve a system of linear equations are considered in this study. The four iteratives approach are Jacobi method, Successive Over Relaxation Method Conjugate Gradient and Preconditioned Conjugate Gradient. This study used symmetric matrices of various sizes, including 3x3, 4x4, and 6x6 matrices. The outcome demonstrates that, out of all the methods, Preconditioned Conjugate Gradient performs the best. When conducting the investigation, a stopping criterion with a tolerance of e~6 was required. The maximum iteration represents the solution once the calculation has attained the required tolerance. The procedure is more effective it has the smallest iteration. This study makes it possible for researchers or analysts to learn how iterative approaches can be used to comprehend the system solution of linear equations.
format	Thesis
qualification_level	Bachelor degree
author	Azmi Hisham, Allisya Farhana
author_facet	Azmi Hisham, Allisya Farhana
author_sort	Azmi Hisham, Allisya Farhana
title	A comparison of the Jacobi method, Successive Over-Relaxation (SOR), Conjugate Gradient (CG), and Preconditioned Conjugate Gradient (PCG) in solving linear systems / Allisya Farhana Azmi Hisham
title_short	A comparison of the Jacobi method, Successive Over-Relaxation (SOR), Conjugate Gradient (CG), and Preconditioned Conjugate Gradient (PCG) in solving linear systems / Allisya Farhana Azmi Hisham
title_full	A comparison of the Jacobi method, Successive Over-Relaxation (SOR), Conjugate Gradient (CG), and Preconditioned Conjugate Gradient (PCG) in solving linear systems / Allisya Farhana Azmi Hisham
title_fullStr	A comparison of the Jacobi method, Successive Over-Relaxation (SOR), Conjugate Gradient (CG), and Preconditioned Conjugate Gradient (PCG) in solving linear systems / Allisya Farhana Azmi Hisham
title_full_unstemmed	A comparison of the Jacobi method, Successive Over-Relaxation (SOR), Conjugate Gradient (CG), and Preconditioned Conjugate Gradient (PCG) in solving linear systems / Allisya Farhana Azmi Hisham
title_sort	comparison of the jacobi method, successive over-relaxation (sor), conjugate gradient (cg), and preconditioned conjugate gradient (pcg) in solving linear systems / allisya farhana azmi hisham
granting_institution	Universiti Teknologi MARA, Terengganu
granting_department	College of Computing, Informatics and Mathematics
publishDate	2023
url	https://ir.uitm.edu.my/id/eprint/96627/1/96627.pdf
_version_	1804890000772300800

A comparison of the Jacobi method, Successive Over-Relaxation (SOR), Conjugate Gradient (CG), and Preconditioned Conjugate Gradient (PCG) in solving linear systems / Allisya Farhana Azmi Hisham

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