Information Moves Slowly
For this smooth discrepancy to be “noticed” by iterative method, the points along way away need to affect each other. This will take N steps to happen as information moves slowly (one grid point per iteration) in Jacobi
Then after impact, one needs to actually correct value
Thus convergence takes N2 iterations
On the other hand, if residual varies rapidly with position, that will be corrected quickly as only needs a few iterations for information to be communicated
Thus rapidly varying residual corresponds to lowest eigenvalue