Not too suprisingly--since that was the purpose of the construction--we see the same sequence of iterates that we saw for the second example:

- Iteration 1:
*x*_{c}= 0.20,*x*= -0.5_{t} - Iteration 2:
*x*_{c}= 0.20,*x*= 0.10_{t} - Iteration 3:
*x*_{c}= 0.10,*x*= 1.50_{t} - Iteration 4:
*x*_{c}= 0.10,*x*= -0.20_{t} - Iteration 5:
*x*_{c}= 0.10,*x*= 0.0_{t} - Iteration 6:
*x*_{c}= 0.0,*x*= -0.10_{t} - Iteration 7:
*x**= 0.0

The question then becomes, how to balance our desire to find a
confirmed minimizer with our desire to "know" enough about the
function to avoid missing a potentially better solution simply because
the approximation may not be sufficiently good to predict a better
solution?

** Next:** An Alternate Outcome:
** Previous:** Second Example Revisited: