This intuitively should make sense.

If I have an f of k for which the phi f of k is equal to 0,

then clearly f of k plus 1 equals f of k plus beta phi f of k.

And since this is 0, this is f of k.

So we see that this f of k is a stationary point.

I cannot move away from it at the

next iteration step, I find exactly the same answer.

Of course this does not prove that, even if phi has a

root, that I'm guaranteed to find it by using this iterative algorithm.

Because this algorithm may or may not converge.

And indeed, finding the sufficient conditions for convergence

of any iterative algorithm is one very important element.

So we're not going to discuss the, in

general, the convergence of an algorithm like this.

There are notions such as contraction mapping, so

if psi, for example, is a contraction mapping,

then I'm guaranteed to find a unique solution

of this optimization, in essence, that I'm performing.

But we are going to look at the convergence property of an

algorithm like this when it takes a specific case of interest.

When I started image restoration.