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lecturenotes10_3

# lecturenotes10_3 - Midpt Algorithm for Bisection 1 Choose...

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Bisection Friday October 3 , 2008

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Root Finding Bisection is a conceptually simple method for finding the root of a function the root of a function is where the function equals zero We will use bisection to find the P rA value from the two equations for CO and VR
Graphically: root

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Finding this root? 1. Choose a starting point (you know the root is between?? ) 2. How can we validate this? f(3) = f(5) = 1. Now choose the midpoint between these 2. Is the root now in [3,4] or [4,5]? 3. Confirm this f(4) = 1. The new interval is now: x = 3 x = 5 x = 4
Tabular Form a b f(a) f(b)

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Unformatted text preview: Midpt Algorithm for Bisection 1. Choose two starting values 2. check to see that the root is between them {sign(f(x1)) ~= to sign(f(x2))} 3. Divide the interval in half 4. Check to see which end of the interval to replace (replace the boundary with the same sign as the function value at the midpoint x) 5. If neither boundary values is the root, bisect again. 6. Repeat 1 through 5 until one of the values is the root. Coding • We will now code the example in class. • See Moodle for the resulting script file....
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lecturenotes10_3 - Midpt Algorithm for Bisection 1 Choose...

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