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

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Presentation on theme: "Golden Section Method Prepared by Shahrzad Kavianirad Submitted to Prof. Dr. Sahand Daneshvar."— Presentation transcript:

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

8

9 Example 2 2 2 θ θ

10

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


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