•Take i=6, so there are 2^6-1=63 unknowns. In the figures to follow, the true solution is a sine curve, shown as a dotted line in the leftmost plot in each row. The approximate solution is a solid line in the same plot. The middle plot shows the error alone. The rightmost plot shows the frequency components of the error.
•Initially, the norm of the vector decreases rapidly, from 1.78 to 1.11, but then decays more gradually, because there is little more error in the high frequencies to damp. Thus, it only makes sense to do 1 or perhaps 2 iterations of S(i) at a time.