So far, we've looked at the use of matrix inversion, the LU decomposition, the Cholesky decomposition, and QR decomposition to solve for systems of linear equations. Should the size of our financial data in the A matrix be large, it can be broken down by a number of schemes so that the solution can converge more quickly using matrix algebra. Quantitative portfolio analysts should be familiar with these methods.
In some circumstances, the solution that we are looking for might not converge. Therefore, you might consider the use of iterative methods. Common methods to solve systems of linear equations iteratively are the Jacobi method, the Gauss-Seidel method, and the SOR method. We will take a brief look at examples of implementing the Jacobi and Gauss-Seidel methods.