The algorithm of the Golden Search method is similar to the algorithm of the Bisection Method (see Bisection Method algorithm). The Golden Search method uses an interval reduction factor that is based on the Fibonacci numbers, instead of just selecting the middle point of the interval for a given interval [x_a,x_n] that contains the minimum value for the function f(x), and the tolerance level as well.

Testing the Golden Search Method

We use the golden search method to find the minimum of a nonlinear function. To test it out as defined above, a new TestBisection() static method has been added and executed. Supporting code and methods are not shown.

           static void TestGoldenSearch();
              {
                 ListBox1.Items.Clear();
                 ListBox2.Items.Clear();
                 double result = Optimization.GoldenSearch(f, t1, t2, 1.0e-5);
                 ListBox1.Items.Add("x = " + result.ToString());
                 ListBox2.Items.Add("f(x) = " + f(result).ToString());
              }