ECE3040 Chapter 9.pdf - Chapter 9 The lecture notes are selected from the public Powerpoint lecture documents provided by Authors Autar Kaw Sri Harsha

# ECE3040 Chapter 9.pdf - Chapter 9 The lecture notes are...

• Notes
• 40

This preview shows page 1 - 11 out of 40 pages.

Chapter 9 The lecture notes are selected from the public Powerpoint lecture documents provided by Authors: Autar Kaw, Sri Harsha Garapati

Subscribe to view the full document.

Golden Section Search Method
Equal Interval Search Method Figure 1 Equal interval search method. x f(x) a b 2 2 (a+b)/2 Choose an interval [a, b] over which the optima occurs Compute and 2 2 b a f If then the interval in which the maximum occurs is otherwise it occurs in 2 2 b a f 2 2 2 2 b a f b a f b b a , 2 2 2 2 , b a a

Subscribe to view the full document.

Golden Section Search Method The Equal Interval method is inefficient when is small. The Golden Section Search method divides the search more efficiently closing in on the optima in fewer iterations. X 2 X l X 1 X u f u f 2 f 1 f l Figure 2. Golden Section Search method
Golden Section Search Method- Selecting the Intermediate Points a b X l X 1 X u f u f 1 f l Determining the first intermediate point a-b b X 2 a X l X 1 X u f u f 2 f 1 f l Determining the second intermediate point a b b a a b b a a b Golden Ratio=> ... 618 . 0 a b

Subscribe to view the full document.

Golden Section Search- Determining the new search region If then the new interval is If then the new interval is All that is left to do is to determine the location of the second intermediate point. X 2 X l X 1 X u f u f 2 f 1 f l ] , , [ 1 2 x x x l ] , , [ 1 2 u x x x ) ( ) ( 1 2 x f x f ) ( ) ( 1 2 x f x f
Example The cross-sectional area A of a gutter with equal base and edge length of 2 is given by ) cos 1 ( sin 4 A 05 . 0 . Find the angle which maximizes the cross-sectional area of the gutter. Using an initial interval of find the solution after 2 iterations. Use an initial . ] 2 / , 0 [ 2 2 2

Subscribe to view the full document.

Solution ) cos 1 ( sin 4 ) ( f 60000 . 0 ) 5708 . 1 ( 2 1 5 5708 . 1 ) ( 2 1 5 97080 . 0 ) 5708 . 1 ( 2 1 5 0 ) ( 2 1 5 2 1 l u u l u l x x x x x x x x The function to be maximized is Iteration 1: Given the values for the boundaries of we can calculate the initial intermediate points as follows: 2 / 0 u l x and x 1654 . 5 ) 97080 . 0 ( f 1227 . 4 ) 60000 . 0 ( f X 2 X l X 1 X u f 2 f 1 X l =X 2 X 2 =X 1 X u X 1 =?
Solution Cont 2000 . 1 ) 60000 . 0 5708 . 1 ( 2 1 5 60000 . 0 ) ( 2 1 5 1 l u l x x x x To check the stopping criteria the difference between and is calculated to be u x l x 97080 . 0 60000 . 0 5708 . 1 l u x x

Subscribe to view the full document.

Solution Cont Iteration 2 97080 . 0 2000 . 1 5708 . 1 60000 . 0 2 1 x x x x u l 0791 . 5 ) 2000 . 1 ( f 1654 . 5 ) 97080 . 0 ( f ) ( ) ( 2 1 x f x f 82918 . 0 ) 6000 . 0 2000 . 1 ( 2 1 5 2000 . 1 ) ( 2 1 5 2 l u u x x x x X l X 2 X u X 1 97080 . 0
• Fall '17
• le yi wang

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern

Ask Expert Tutors You can ask 0 bonus questions You can ask 0 questions (0 expire soon) You can ask 0 questions (will expire )
Answers in as fast as 15 minutes