446proj1 - MATH 446 / OR 481 SAUER SPRING 2010 Project 1...

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MATH 446 / OR 481 SAUER SPRING 2010 Project 1 Applying the Bisection Method in Double Precision Your job is to find the real root of f 1 ( x ) = 10(1 - cos 4 x )(2 cos 2 x - 4 cos 5 x + 6 cos 2 x + 3 cos x sin 2 2 x - 12 cos x sin 4 x - 4) +32 cos 9 x - 48 cos 6 x + 96 cos 3 x - 72 cos x - 4 that lies between 0 and 1 . There is only one such root. Our fundamental ques- tion: If you calculate in double precision (as Matlab does automatically), can you guarantee that your answers are correct to double precision? 1. Apply the Bisection Method four times to calculate the root, using starting intervals [0 , 1] , [0 . 1 , 1] , [0 . 2 , 1] , and [0 . 3 , 1] respectively. Calculate the root to as many correct places as you can. For each starting interval, report the Bisection Method’s best guess for the root, to as many decimal places as you can. (You should use format long in Matlab to see plenty of deci- mal places.) Report your backward, or checking, error for each of the four runs. (We are mainly interested in the order of magnitude of the backward
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This note was uploaded on 10/27/2010 for the course MATH 446 taught by Professor Staff during the Spring '08 term at George Mason.

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