**Example 4.** Use
Powell's method to find the minimum of ,

This example is referred to as Rosenbrock's parabolic valley, circa
1960.

**Solution 4.**

Enter the function and graph the surface .

Perform the Powell method search for the minimum.

Let us compare this answer with *Mathematica*'s built in
procedure **FindMinimum**.

**Observation.** Even
*Mathematica* is having a hard time finding the minimum
of .

Since the function is "flat" near the minimum, the best way to
achieve better accuracy is to increase the WorkingPrecision, i.e.
use extended precision in the numerical computations.

(c) John H. Mathews 2004