Because we have a quadratic rate of convergence we

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

This document was uploaded on 03/17/2014 for the course ELECTRICAL 6.006 at MIT.

Ask a homework question - tutors are online