The feature of the basic theorems that are related to the numerical computation and some examples of how to use them are introduced through the simulation. The new iterative techniques for solving the algebraic Riccati equation and algebraic Lyapunov equation are used for weakly-coupled systems as an application. It is shown that the free numerical application tool which is called Octave is very powerful tool and it is available for the understanding of the numerical computation for undergraduate students in the early learning stage.