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Let A i 4 -1 0 0 -1 4 -1 0 0 -1 4 -1 0 0 -1 4 0 0 0 0 " 0 0 0 0 0 0 0 0 0 0 0 0 -/ = -1

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

Solution for problem 11 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 11

Let A i 4 -1 0 0 -1 4 -1 0 0 -1 4 -1 0 0 -1 4 0 0 0 0 " 0 0 0 0 0 0 0 0 0 0 0 0 -/ = -1 0 0 0 0 -1 0 0 0 0 -1 0 0 0 0 -1 and O = Form the 16 x 16 matrix A in partitioned form. A = A\ -I O 0 -I A\ -/ 0 0 -1 A\ -I 0 o -/ Ai Let b = (1,2,3,4,5,6,7,8,9,0, 1,2,3.4.5,6)'.a. Solve Ax = b using the conjugate gradient method with tolerance 0.05. b. Solve Ax = b using the preconditioned conjugate gradient method with C _l = Z)_1T 2 and tolerance 0.05. c. Is there any tolerance for which the methods of part (a) and part (b) require a different number of iterations?

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Chapter 7.6, Problem 11 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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Let A i 4 -1 0 0 -1 4 -1 0 0 -1 4 -1 0 0 -1 4 0 0 0 0 " 0 0 0 0 0 0 0 0 0 0 0 0 -/ = -1