Ee1031cS10

# Ee1031cS10 - Example 5 root finding f x 0 x f f x e x v min...

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Example 5: root finding () 0 f x x f x f ex v min ( ) x Fx def f xe xv  0 ' F x f x UCLA SEAS EE103 (SEJ) SLIDES 1C 1 Taylor’s 0 th Order Theorem (Mean Value Theorem) f f x f x x x ( ) fx fx f xf x x x x x  x x , x x , , 0 '( ) ' ( ) ( ) ' th xx f Mean Value Theorem x x f x f x f xxT a ylor s Order Theorem  UCLA SEAS EE103 (SEJ) SLIDES 1C 2 (;) ' ( ) ' 1 st f xL x x f x fxxx T aylor s Order Approximation 

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() () 0 fafb ()( ) 0 xa b f x  Another example of the need for good algorithms ( , )(   mx        aa b b () ( ) ' ( ) ( ) , f x f m f xm  | ' | [ fx Mx a b  |( ) , [ , ] |() | |' ( ) | | | | | | | 2 M f xf m f x m M x m b a  UCLA SEAS EE103 (SEJ) SLIDES 1C 3 , Another example of the need for good algorithms |() () | [ fx fm x ab [ , ]  || 2 / M ba o r M   2 2/ 2 baM MN N  UCLA SEAS EE103 (SEJ) SLIDES 1C 4
ex: Let the absolute value of the derivative be bounded

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Ee1031cS10 - Example 5 root finding f x 0 x f f x e x v min...

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