Example 1.  Find the minimum of the function    on the interval    using the quadratic search method.

Solution 1.

Set  ,  and  ,  and  .  

We must decide whether to use   or change the step size to   or    and recompute some of these values.  

The step size has not changed and we now compute .  

We use the "latest three values" and change the step size and continue the iteration with the following three values used in the interpolating quadratic.

The last three values will be labeled by the subroutine.  The list of computations obtained by using the Quadraticearch subroutine are:  

Let us compare these answers with Mathematica's subroutine FindMinimum.

(c) John H. Mathews 2004