|
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
|
