HW 4 Solutions

# HW 4 Solutions - MIT OpenCourseWare http/ocw.mit.edu 18.085...

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MIT OpenCourseWare http://ocw.mit.edu 18.085 Computational Science and Engineering I Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .

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HOMEWORK 4 II.3.7 1 0 1 1 A = 1 2 1 3 The normal equation is A t = Au ˆ A t b , so 1 ± 0 1 1 1 1 1 1 0 1 2 3 1 2 1 3 4 ± C 1 1 1 1 1 = D 0 1 2 3 ± 0 1 The solution is 3 1 ± II.3.8 p = 1 0 3 1 1 3 = 1 2 1 1 3 2 1 ± 0 which lies on 3 x . The error is 1 1 e = 1 1 and 1 1 A t 1 1 1 1 e = = 0 0 1 2 3 ± 1 1 II.3.12 In this case 1 0 0 1 1 1 A = 1 2 4 1 3 9 1
HOMEWORK 4 2 The “unsolvable equations” are 1 0 0 1 1 1 1 2 4 D 4 C 1 = 0 E 1 3 9 ⎥⎣ 1 The normal equation equat ion is 1 0 0 4 1 1 1 1 C 1 1 1 1 1 1 1 1 0 1 2 3 D = 0 1 2 3 1 2 4 0 0 1 4 9 ⎤ ⎡ ⎦⎢ E ⎦ ⎣ 0 1 4 9 1 3 9 1 The “unsolvable equations” for the cub ic will be a 4 4 (nonsingular

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HW 4 Solutions - MIT OpenCourseWare http/ocw.mit.edu 18.085...

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