HW3 Solution

# HW3 Solution - ME218: Solutions to Homework 3 Problem1. f (...

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ME218: Solutions to Homework 3 Problem1 . 11 1 () 0 ( ) ( ) ( ) n nn n n n n n n fx f x x x x x ++ + ʹ = + − ⇒ = ʹ For /4 2 1 x fx e x =+ , we have 0 . 2 5 2 x e x ʹ = + 00 0 1 1( ) 0 . 7 7 8 8 , ( ) 1 . 8 0 5 3 0 . 5 6 8 6 xf x f x x ʹ = = = = Iteration n x n n ʹ 1 n x + 1 1 0.7788 1.8053 0.5686 2 0.5686 0.1908 0.9203 0.3613 3 0.3613 0.4417 0.4942 0.2719 4 0.2719 0.0082 0.3103 0.2454 The approximation result after 4 iterations is 0 . 2454 . Problem2 1 ( ) ( ) ( ) 0 ( ) ii i i i i i i i i i x x x x x x xx f x f x −− + = + = . For 01 , 0 , 1 x e x = = = , we have 2 ()1 ,()- 0 . 6 3 2 1 0 . 6 1 2 7 x == = Iteration 1 i x i x 1 i i 1 i x + 1 0 1 1.0000000 -0.6321205 0.6126998 2 1 0.6126998 -0.6321205 -0.0708139 0.5638383 3 0.6126998 0.5638383 -0.0708139 0.0051824 0.5671703 The approximation result after 3 iterations is 4 0.5671703 x . If 0.5671433 Actual x , the relative error of the solution is 3 0.5671703 0.5671433 100% 4.76 10 % 0.5671433 Actual Actual x x δ Δ− = × = ×

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Problem3. (a) 0000 9 15 21 27 138, 18 30 42 54 27 45 63 81 cd dc ΡΤ ΢Υ == ΣΦ rr . They are not equal. The former is a scalar while the latter is a 44 × matrix. (b) 3 4 Ib = r r , which is equal to b r . 1 2 x Ix x = r r , which is equal to ) x r . (c) 12 1 3 2 1 4 3 2 1 1 0 , ( ) ( ) ( ) 32 0 4 0 1 0 1 EA E EA E EEA E EEEA −−
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## This note was uploaded on 12/14/2011 for the course ME 218 taught by Professor Unknown during the Fall '08 term at University of Texas at Austin.

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HW3 Solution - ME218: Solutions to Homework 3 Problem1. f (...

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