Numerical Analysis

The function is unimodal on , if there exists a unique number such that is decreasing on , and is increasing on . Golden Ratio: If is known to be unimodal on , then it is possible to replace the interval with a subinterval on which takes on its minimum value. One approach is to select two interior points . This results in . The condition that is unimodal guarantees that the function values and are less than . If , then the minimum must occur in the subinterval , and we replace b with d and continue the search in the new subinterval . If , then the minimum must occur in the subinterval , and we replace a with c and continue the search in the new subinterval . These choices are shown in Figure 1 below. If , then squeeze from the right and use the new interval and the four points . If , then squeeze from the left and use the new interval and the four points . ...