This Demonstration computes the exact McCabe–Thiele diagram using matrix inversion. The horizontal lines represent the theoretical equilibrium stages in the absorption column. The successive over-relaxation (SOR) method is compared to the exact solution by plotting the cumulative squared error versus the number of iterations. The parameter is chosen to be between and . For (see the last snapshot showing large growing error), you can see that the SOR method fails to give good results. A theorem of Kahan states that the SOR method will converge only if is chosen in the interval . For , the SOR method is identical to the Gauss–Seidel technique.