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Unformatted text preview: Homework 5 Solution 1. Consider the following function: f ( x ) = 1 + 4 x 2 x 2 + cos x (a) [2pt] Find an maximum using three iterations of the Golden Section search with initial guesses x l = 5 and x u = 5. (b) [2pt] Find an maximum using three iterations of quadratic interpolation with initial guesses x = 5 , x 1 = 2, and x 2 = 3. (c) [2pt] Find an maximum using three iterations of the Newtons method with an initial value x = 5. Solution. (a) Golden Section Method Iteration 1:Given initial guesses x l = 5 , x u = 5 d = 5 1 2 ( x u x l ) = 6 . 18 x 1 = x l + d = 5 + 6 . 18 = 1 . 18 , x 2 = x u d = 1 . 18 f ( x 1 ) = 3 . 3161 , f ( x 2 ) = 6 . 1239 f ( x 2 )is smaller,let x l = x 2 = 1 . 18 , x 2 = x 1 = 1 . 18 Iteration 2: d = 5 1 2 ( x u x l ) = 3 . 8195 x 1 = x l + d = 2 . 6395 , f ( x 1 ) = 3 . 2521 f ( x 1 )is smaller,let x u = x 1 = 2 . 6395 , x 1 = x 2 = 1 . 18 Iteration 3: d = 5 1 2 ( x u x l ) = 2 . 3606 x 2 = x u d = 0 . 2789 f ( x 2 ) = f (0...
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This note was uploaded on 11/14/2011 for the course EAME 250 taught by Professor Lee during the Spring '11 term at Case Western.
 Spring '11
 LEE

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