Chapter 15, Problem 16P

Develop an M-file to implement parabolic interpolation to locate a minimum. Test your program with the same problem as Example 13.2. The function should have the following features:

• Base it on two initial guesses, and have the program generate the third initial value at the midpoint of the interval.

• Check whether the guesses bracket a maximum. If not, the function should not implement the algorithm, but should return an error message.

• Iterate until the relative error falls below a stopping criterion or exceeds a maximum number of iterations.

• Return both the optimal x and $f\left(x\right)$.

• Use a bracketing approach (as in Example 13.2) to replace old values with new values.