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Approximate solutions to the following linear systems Ax = b to within I0-5 in the norm

Numerical Analysis | 10th Edition | ISBN: 9781305253667 | Authors: Richard L. Burden J. Douglas Faires, Annette M. Burden ISBN: 9781305253667 457

Solution for problem 9 Chapter 7.6

Numerical Analysis | 10th Edition

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Numerical Analysis | 10th Edition | ISBN: 9781305253667 | Authors: Richard L. Burden J. Douglas Faires, Annette M. Burden

Numerical Analysis | 10th Edition

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Problem 9

Approximate solutions to the following linear systems Ax = b to within I0-5 in the norm. (i) 4, a, , = 1, when 0, when j i and i 1,2,... ,16, + 1 and / = 1,2,3,5,6,7,9, 10, 11, 13, 14, 15, - 1 and / =2,3,4,6,7,8, 10, 11, 12, 14, 15, 16, + 4and/ = 1,2,... , 12, 4 and / = 5, 6,... ,16, J = J = j = j = otherwise and a. c. d. b = (1.902207, 1.051143, 1.175689,3.480083,0.819600. -0.264419, -0.412789, 1.175689,0.913337,-0.150209,-0.264419, 1.051143, 1.966694, 0.913337, 0.819600, 1.902207)' (ii) 'i.J < 1, when J - i 1 and i j i \ and i and (iii) 4, when j i and i 1,2,... , 25, 1,2,3,4, 6,7.8,9, 11, 12, 13, 14, 16, 17, 18, 19, 21, 22, 23, 24, 2,3,4,5,7,8,9, 10, 12, 13, 14, 15, 17, 18, 19, 20. 22, 23,24, 25, j = i + 5 and i = 1,2,... , 20. j i 5 and / = 6, 7,... . 25, 0, otherwise b = (1,0,-1,0,2, 1.0. -1.0,2, 1,0, -1,0,2, 1,0, -1,0,2, 1,0, -1,0,2)' 2i, when j = i and / = 1, 2,... , 40, /./ = / +I andi = 1,2,... ,39, 1, when < ^ y = / I and i =2,3,... , 40, 0, otherwise CliJ = and hi 1.5/ - 6, for each i 1.2,... ,40 Use the Jacobi method. b. Use the Gauss-Seidel method. Use the SOR method with co 1.3 in (i), co 1.2 in (ii), and co 1.1 in (iii). Use the conjugate gradient method and preconditioning with

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MECH 1321 Spring, 2016 MECH 1321: STATICS Class Reference Number: 13749 Textbook: Engineering Mechanics: Statics 14 Edition by R.C. Hibbeler Required Material: Mastering Engineering Access Code Class/Lab Meeting: MW, 3:00 pm to 4:20 pm Class Room: College of Business Administration Room 312 Prerequisite: MATH 1411 Calculus Recommended Pre Course: PHYS 2420 Physics I Instructor: Dr. Barry A. Benedict, babenedict@utep.edu Phone : 915­747­5604 Office Hours: TB

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Chapter 7.6, Problem 9 is Solved
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Textbook: Numerical Analysis
Edition: 10
Author: Richard L. Burden J. Douglas Faires, Annette M. Burden
ISBN: 9781305253667

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Approximate solutions to the following linear systems Ax = b to within I0-5 in the norm