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Unformatted text preview: Numerical Methods  Homework 2 CS257 September 13, 2006 All computer problems are worth 2 points. All remaining problems are worth 1 point. 1. Solution 2.2 14: The exact sum of these four numbers is 0.31491. We will use this to calculate relative error. Next, we add the numbers in ascending order and computer the error fl(0 . 00051 + 0 . 0034) = 0 . 0039 fl(0 . 0039 + 0 . 061) = 0 . 065 fl(0 . 065 + 0 . 25) = 0 . 32 err =  . 32 . 31491  . 31491 ≈ 1 . 62 × 10 2 Finally, we compute the sum by adding the numbers in reverse order and compute the error in this case fl(0 . 25 + 0 . 061) = 0 . 31 fl(0 . 31 + 0 . 0034) = 0 . 31 fl(0 . 31 + 0 . 00051) = 0 . 31 err =  . 31 . 31491  . 31491 ≈ 1 . 56 × 10 2 Adding the numbers in reverse order gives better results. 2. Solution 2.2 25: Following the hint in the book, we note that xy is computed as fl(fl( x ) fl( y )). z = fl(fl( x ) fl( y )) = (1 + δ 3 )((1 + δ 1 ) x )((1 + δ 2 ) y )) ≈ (1 + δ 1 + δ 2 + δ 3 ) xy Assuming that neither x nor y is zero allows us to read off the relative error as  δ 1...
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This note was uploaded on 09/15/2008 for the course CS 257 taught by Professor Thomaskerkhoven during the Fall '05 term at University of Illinois at Urbana–Champaign.
 Fall '05
 ThomasKerkhoven

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