Comparison of Gaussian Elimination and Cholesky Decomposition Solving A Linear System Of Equation. - Nzabonimpa, Godfrey (Kabale University, 2024)
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.