q1s - n log 2 > log 1000, so n > log...

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Numerical Analysis/Quiz #1/September 14, 2009 SOLUTIONS 1. After n iterations, error is at most ( b - a ) / 2 n . In this case, we need to find n such that 1 / 2 n < 10 - 3 , that is 2 n > 1000. We could determine this by counting on our fingers: 2 9 = 512 < 1000 < 1024 = 2 10 , so n 10. More generally, taking logs (to any base) of both sides gives
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Unformatted text preview: n log 2 &gt; log 1000, so n &gt; log 1000 log 2 9 . 97. Since n must be an integer, we need n 10 iterations. 2. a b m 2 3 2 . 5 2 2 . 5 2 . 25 2 2 . 25 2 . 125 2 . 125 2 . 25 2 . 1875 The estimate is 2 . 1875 with error at most (3-2) / 2 4 = 0 . 0625....
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