Steepest descent

1.

Use Maple to implement steepest descent, following the example on page 420 of the text. Go step by step to make sure you can duplicate the results in the book.

2.

Use the set of commands you just debugged (and any procedures you wrote) to apply one iteration of steepest descent to the original problem, starting from (0,0,0) again.

Hint: As the book implies, choosing $\alpha_3$ is an art. In this case, I recommend 3. If you choose another value, make sure you know what to do if the critical point does not lie between $\alpha1$ and $\alpha3$.

Hint: for help finding the critical point, see Exercise 6 on page 422.

3.

Perform a few steps of Newton's method and see if convergence is going any better from this position.