1. Numerical Methods Golden Section Search Method - Example http://nm

2. For more details on this topic
Go to
Click on Keyword
Click on Golden Section Search Method

3. You are free
to Share – to copy, distribute, display and perform the work
to Remix – to make derivative works

4. Under the following conditions
Attribution — You must attribute the work in the manner specified by the author or licensor (but not in any way that suggests that they endorse you or your use of the work).
Noncommercial — You may not use this work for commercial purposes.
Share Alike — If you alter, transform, or build upon this work, you may distribute the resulting work only under the same or similar license to this one.

5. Example . 2 2   2
The cross-sectional area A of a gutter with equal base and edge length of 2 is given by (trapezoidal area):
Find the angle  which maximizes the cross-sectional area of the gutter. Using an initial interval of find the solution after 2 iterations.
Convergence achieved if “ interval length ” is within

6. Solution The function to be maximized is
Iteration 1: Given the values for the boundaries of
we can calculate the initial intermediate points as follows:
XL=X2
X2=X1 Xu X2 XL X1 Xu f2 f1
X1=?

7. Solution Cont
To check the stopping criteria the difference between and is calculated to be

8. Solution Cont
Iteration 2 XL X2 Xu X1

9. Theoretical Solution and Convergence
Iteration xl xu x1 x2
f(x1)
f(x2)  1
0.0000
1.5714
0.9712
0.6002
5.1657
4.1238 2
1.2005
5.0784 3
0.8295
4.9426 4
1.0588
5.1955
0.3710 5
1.1129
5.1740
0.2293 6
1.0253
5.1937
0.1417 7
1.0794
5.1908
0.0876 8
1.0460
5.1961
0.0541 9
1.0381
5.1957
0.0334
The theoretically optimal solution to the problem happens at exactly 60 degrees which is radians and gives a maximum cross-sectional area of

10. The End

11. Acknowledgement
This instructional power point brought to you by
Numerical Methods for STEM undergraduate
Committed to bringing numerical methods to the undergraduate

12. For instructional videos on other topics, go to
This material is based upon work supported by the National Science Foundation under Grant # Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

13. The End - Really