Comparison of Gaussian Elimination and Cholesky Decomposition Solving A Linear System Of Equation.
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 Gaussia...
Saved in:
| Main Author: | |
|---|---|
| Format: | Thesis |
| Language: | en_US |
| Published: |
Kabale University
2024
|
| Subjects: | |
| Online Access: | http://hdl.handle.net/20.500.12493/1652 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1803933476670406656 |
|---|---|
| author | Nzabonimpa, Godfrey |
| author_facet | Nzabonimpa, Godfrey |
| author_sort | Nzabonimpa, Godfrey |
| 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 Cho!sky 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:20.500.12493-1652 |
| institution | KAB-DR |
| language | en_US |
| publishDate | 2024 |
| publisher | Kabale University |
| record_format | dspace |
| spelling | oai:idr.kab.ac.ug:20.500.12493-16522024-06-12T12:50:06Z Comparison of Gaussian Elimination and Cholesky Decomposition Solving A Linear System Of Equation. Nzabonimpa, Godfrey Comparison Gaussian Elimination Cholesky Decomposition Solving Linear System Equation 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 Cho!sky 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. 2024-01-15T11:53:32Z 2024-01-15T11:53:32Z 2022 Thesis Nzabonimpa, Godfrey (2022). Comparison of Gaussian Elimination and Cholesky Decomposition Solving A Linear System Of Equation. Kabale: Kabale University. http://hdl.handle.net/20.500.12493/1652 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 Solving Linear System Equation Nzabonimpa, Godfrey Comparison of Gaussian Elimination and Cholesky Decomposition Solving A Linear System Of Equation. |
| title | Comparison of Gaussian Elimination and Cholesky Decomposition Solving A Linear System Of Equation. |
| title_full | Comparison of Gaussian Elimination and Cholesky Decomposition Solving A Linear System Of Equation. |
| title_fullStr | Comparison of Gaussian Elimination and Cholesky Decomposition Solving A Linear System Of Equation. |
| title_full_unstemmed | Comparison of Gaussian Elimination and Cholesky Decomposition Solving A Linear System Of Equation. |
| title_short | Comparison of Gaussian Elimination and Cholesky Decomposition Solving A Linear System Of Equation. |
| title_sort | comparison of gaussian elimination and cholesky decomposition solving a linear system of equation |
| topic | Comparison Gaussian Elimination Cholesky Decomposition Solving Linear System Equation |
| url | http://hdl.handle.net/20.500.12493/1652 |
| work_keys_str_mv | AT nzabonimpagodfrey comparisonofgaussianeliminationandcholeskydecompositionsolvingalinearsystemofequation |