A function, F, is a function of the independent variable x. The value of x that will
minimize F is to be determined. There are lower and upper bounds that bracket the
minimum, XL and Xu.
The function F has been evaluated at XL and Xu and therefore the corresponding values
of FL and Fu are known.
100
90
Y 80 -
70
60-
>, 50
40
30
YL V/
20 /
Y3
Y,
10-
Y2
1 2 3 4 5 6 7 8 9 10
XL Xi X2 X3 X,
Figure 3.2: Illustration of the Golden Section Method
The golden section method proceeds by choosing two intermediate points between XL
and Xu (see figure 3.2). As stated earlier, the function is assumed to be uni-modal,
therefore X1 or X2 will form a new bound on the minimum. Because F1 is greater than F2
it forms a new lower bound, which produces a new set of bounds X, and Xu. X, is the
new lower bound and a new point X3 is chosen and evaluated for F3. When comparing F2