Unformatted text preview: n such that there is a ﬁxed point of f in the interval [ n,n + 1) = { x ∈ IR : n ≤ x < n + 1 } . The number of times your algorithm calls the function f should be O (log  f (0)  ). Your pseudocode should include pre and postconditions. If you use a loop, you should also include a loop invariant in the pseudocode that you can use for part (c), below. (d) Prove that the algorithm given in part (b) is correct. Note: you do not have to prove that your algorithm calls f O (log  f (0)  ) times, but it should be true in order for your algorithm to get full marks. Example: The graph below shows the strictly decreasing function f ( x ) = (7x ) 3 30 . It has a ﬁxed point between 2 and 3, so if your algorithm is run with this function f , it should output 2. 1...
View
Full Document
 Winter '16
 Calculus, Algorithms, Continuous function, strictly decreasing function

Click to edit the document details