Because we have a quadratic rate of convergence we

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Unformatted text preview: use we threw away information (taking the floor) before performing another operation. Instead, we first calculate B = A3 , then compute C = B 1/4 using the formula from part (a) to continually improve our estimate. Because we have a quadratic rate of convergence, we will improve our estimate Θ(log d) times, and each time we will perform a constant number of arithmetic operations. Note: This is equivalent to applying Newton’s Method to the function f (x) = x4 − A3 , but does not require you to rederive the equation for xi+1 in terms of xi . Θ(d) Solution: Use the comparison method from part (c) to do binary search. This requires us to do Θ(1) operations for each of the bits in the result, for a total of Θ(d) operations. 10 6.006 Quiz 2 Solutions Name 11 Problem 5. The Tourist [15 points] Your new startup, Bird Tours, brings people around Boston in a new aviation car that can both drive and fly. You’ve constructed a weighted directed graph G = (V, E, w) representing the best time to drive or fly between various...
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