Study about three methods of solving linear equations

Since linear equations have great contribution in the study of the numerical pde, therefore it has been studied for ages. In this paper, I will write a survey that contains three methods of solving the linear equations, as well as the implementations of these three methods. After that, other methods of finding the inverse matrix of a specific sparse matrix will be shown. Three methods are the Gauss elimination, LU decomposition and Cholesky decomposition. These algorithms can be implemented by invoking related built-in functions in MATLAB. The LU decomposition, as a method of decomposing a matrix into an upper triangular matrix and a lower triangular matrix, can be performed by calling the function lu() in MATLAB. Cholesky factorization can be achieved by calling the function chol() in MATLAB.