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 |
| Published: |
Kabale University
2024
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| Subjects: | |
| Online Access: | http://hdl.handle.net/20.500.12493/1702 |
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| Summary: | 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. |
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