1. Golden Section Method Prepared by Shahrzad Kavianirad Submitted to Prof. Dr. Sahand Daneshvar

2. Outline What is the Golden Section Search intermediate points Golden Ratio Algorithm example

3. Golden Section Method What is the Golden Section Search method used for and how does it work?  Unimodal function

4. How are the intermediate points in the Golden Section Search determined? a ba b a-b

5. Does the Golden Section Search have anything to do with the Golden Ratio?

6. ab b a

7. The Golden Section Search Algorithm

9. Example 2 2 2 θ θ

11. It is greater then ε The process is repeated in the second iteration.

12. Example 0.6 Max area when θ=0.9 or 51.6 degree

13. Example Iteration 10.000001.57080.970810.599995.16544.12261.5708 20.599991.57081.20000.970815.07915.16540.97081 30.599991.20000.970810.829175.16544.94180.59999 40.829171.20001.05830.970815.19555.16540.37081 50.970811.20001.11241.05835.17435.19550.22918 60.970811.11241.05831.02495.19555.19360.14164 71.02491.11241.07901.05835.19095.19550.08754 81.02491.07901.05831.04565.19555.19610.05410 91.02491.05831.04561.03775.19615.19570.03344

14. Golden Section Method