Unformatted text preview: 3 . How many iterations were needed? (provide the MATLAB code) 8. Use the theoretical result given in class (  pp n  ≤ k n ( ba )) to estimate the number of iterations required to achieve 103 accuracy. Why is this number diﬀerent than the one obtained in 7. ? • Let f ( x ) = ex 1. Sketch the graph of f ( x ). 2. Find f ([ 1 3 , 1]) 3. Is it true that f ([ 1 3 , 1]) ⊂ [ 1 3 , 1]? What can you conclude about the existence of a ﬁxed point? 4. Find max x ∈ [ 1 3 , 1]  f ( x )  . 5. Find a number k ∈ (0 , 1) such that  f ( x )  ≤ k for all x ∈ ± 1 3 , 1 ² 6. What can you conclude about using a ﬁxed point iteration. 7. Find the ﬁxed point with accuracy 103 . How many iterations were needed? (provide the MATLAB code) 8. Use the theoretical result given in class (  pp n  ≤ k n ( ba )) to estimate the number of iterations required to achieve 103 accuracy. 1...
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 Spring '10
 THOMAS
 matlab

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