Test Case

Each of the solution methods we will define in the EqnSolver class will be tested using the following 4x4 system of equations.

Equation 19.3

During the development of this chapter, the solution methods were tested over a wide variety of systems of equations, but only results for the system of equations shown in Eq. (19.3) will be presented in this chapter. Eq. (19.4) shows the solution vector for this system of equations.

Equation 19.4

There is a problem with the system of equations shown in Eq. (19.3). The three methods we will use, Gauss-Jordan elimination, Gaussian elimination , and Lower-Upper (LU) decomposition, are unstable under certain circumstances. One of those circumstances is when the top-left diagonal element is zero, as it is (intentionally) for our test problem. Round-off error is another way in which the system can become unstable. One of the ways that stability can be restored to the solution process is by using a technique called pivoting.