A Comparison of Gaussian Elimination and Cholesky Decomposition Methods in Solving a System of Linear Equations.
There are several methods of solving a system of linear equations,. some of which are direct methods and others are iterative methods. In this work, .we study direct methods specifically Gaussian elimination and Cholesky decomposition and make a comparison between the two. It is found out that Gauss...
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| Format: | Thesis |
| Language: | en_US |
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Kabale University
2024
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| Online Access: | http://hdl.handle.net/20.500.12493/1702 |
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| author | Niringiye, Richard |
| author_facet | Niringiye, Richard |
| author_sort | Niringiye, Richard |
| collection | KAB-DR |
| description | There are several methods of solving a system of linear equations,. some of which are direct methods and others are iterative methods. In this work, .we study direct methods specifically Gaussian elimination and Cholesky decomposition and make a comparison between the two. It is found out that Gaussian elimination is an algorithm in linear algebra for solving a system of linear equations and can also be used to find the rank of a matrix, to calculate the determinant of a matrix, and to calculate the inverse of an invertible square matrix Whereas Cholesky decomposition is a decomposition of a Hermitian, positive-definite matrix into the product of a lower triangular matrix and its conjugate transpose, which is useful for efficient numerical solutions. |
| format | Thesis |
| id | oai:idr.kab.ac.ug:20.500.12493-1702 |
| institution | KAB-DR |
| language | en_US |
| publishDate | 2024 |
| publisher | Kabale University |
| record_format | dspace |
| spelling | oai:idr.kab.ac.ug:20.500.12493-17022024-06-12T12:50:27Z A Comparison of Gaussian Elimination and Cholesky Decomposition Methods in Solving a System of Linear Equations. Niringiye, Richard Comparison Gaussian Elimination Cholesky Decomposition Methods Solving System Linear Equations There are several methods of solving a system of linear equations,. some of which are direct methods and others are iterative methods. In this work, .we study direct methods specifically Gaussian elimination and Cholesky decomposition and make a comparison between the two. It is found out that Gaussian elimination is an algorithm in linear algebra for solving a system of linear equations and can also be used to find the rank of a matrix, to calculate the determinant of a matrix, and to calculate the inverse of an invertible square matrix Whereas Cholesky decomposition is a decomposition of a Hermitian, positive-definite matrix into the product of a lower triangular matrix and its conjugate transpose, which is useful for efficient numerical solutions. 2024-01-17T08:42:04Z 2024-01-17T08:42:04Z 2021 Thesis Niringiye, Richard (2021). A Comparison of Gaussian Elimination and Cholesky Decomposition Methods in Solving a System of Linear Equations. Kabale: Kabale University. http://hdl.handle.net/20.500.12493/1702 en_US Attribution-NonCommercial-NoDerivs 3.0 United States http://creativecommons.org/licenses/by-nc-nd/3.0/us/ application/pdf Kabale University |
| spellingShingle | Comparison Gaussian Elimination Cholesky Decomposition Methods Solving System Linear Equations Niringiye, Richard A Comparison of Gaussian Elimination and Cholesky Decomposition Methods in Solving a System of Linear Equations. |
| title | A Comparison of Gaussian Elimination and Cholesky Decomposition Methods in Solving a System of Linear Equations. |
| title_full | A Comparison of Gaussian Elimination and Cholesky Decomposition Methods in Solving a System of Linear Equations. |
| title_fullStr | A Comparison of Gaussian Elimination and Cholesky Decomposition Methods in Solving a System of Linear Equations. |
| title_full_unstemmed | A Comparison of Gaussian Elimination and Cholesky Decomposition Methods in Solving a System of Linear Equations. |
| title_short | A Comparison of Gaussian Elimination and Cholesky Decomposition Methods in Solving a System of Linear Equations. |
| title_sort | comparison of gaussian elimination and cholesky decomposition methods in solving a system of linear equations |
| topic | Comparison Gaussian Elimination Cholesky Decomposition Methods Solving System Linear Equations |
| url | http://hdl.handle.net/20.500.12493/1702 |
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