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Numerical Methods Golden Section Search Method - Example nm.mathforcollege

Numerical Methods Golden Section Search Method - Example http://nm.mathforcollege.com. For more details on this topic Go to http ://nm.mathforcollege.com Click on Keyword Click on Golden Section Search Method . You are free. to Share – to copy, distribute, display and perform the work

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Numerical Methods Golden Section Search Method - Example nm.mathforcollege

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  1. Numerical MethodsGolden Section Search Method - Examplehttp://nm.mathforcollege.com

  2. For more details on this topic • Go to http://nm.mathforcollege.com • 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 http://nm.mathforcollege.com

  6. f1 f2 X2 X2=X1 X1 XL=X2 XL Xu Xu 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: X1=? http://nm.mathforcollege.com

  7. Solution Cont To check the stopping criteria the difference between and is calculated to be http://nm.mathforcollege.com

  8. X2 XL Xu Solution Cont Iteration 2 X1 http://nm.mathforcollege.com

  9. Theoretical Solution and Convergence The theoretically optimal solution to the problem happens at exactly 60 degrees which is 1.0472 radians and gives a maximum cross-sectional area of 5.1962. http://nm.mathforcollege.com

  10. The End http://nm.mathforcollege.com

  11. Acknowledgement This instructional power point brought to you by Numerical Methods for STEM undergraduate http://nm.mathforcollege.com Committed to bringing numerical methods to the undergraduate

  12. For instructional videos on other topics, go to http://nm.mathforcollege.com This material is based upon work supported by the National Science Foundation under Grant # 0717624. 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

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