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Perform only two steps ofthe conjugate gradient method with C = C _1 == / on each ofthe

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

Solution for problem 5 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 5

Perform only two steps ofthe conjugate gradient method with C = C _1 == / on each ofthe following linear systems. Compare the results in parts (b) and (c) to the results obtained in parts (b) and (c) of Exercise 1 of Section 7.3 and Exercise 1 of Section 7.4. a. c. e. 3xi - X2+ X3 = 1. X\ -f- 6x2 T 2x3 = 0, X| + 2x2 + 7x3 = 4. 10x| + 5x2 = 6, 5xi -(- 10x2 4x3 = 25, - 4X2 + 8X3 - X4 = -11, X3 + 5x4 = 11- X2 T X3 -{- X5 = 6, 3x2 T X3 -f- X4 =6, X2 + 5x3 X4 X5 = 6, X2 X3 + 4x4 6, X3 + + 4x5 6. b. d. 4X, i xi f. 10xi X2 =9, X| + 10x2 2x3 7, 2x2 4" IOX3 6. 4xi + X2 - X3 -f X4 = -2, Xj + 4X2 X3 X4 = 1, X] X2 T 5x3 4" X4 = 0, xi X2 4- X3 4- 3x4 = 1 4xi X2 x1 4- 4X2 - -D - X2 4- 4X3 4- 4x4 X5 = 0, = 5. = 0, = 6, *1 X4 4- 4x5- -^6 = -2, - X54-4X6 = 6

Step-by-Step Solution:
Step 1 of 3

L27 - 8 Indeterminate Differences (∞−∞ ) ex. Consider the following: ▯ ▯ ▯ ▯ 1 1 2 1 m x→0 ix− x = l x→0 x − x = ▯ ▯ 1 ex. x→0+ x − cscx

Step 2 of 3

Chapter 7.6, Problem 5 is Solved
Step 3 of 3

Textbook: Numerical Analysis
Edition: 10
Author: Richard L. Burden J. Douglas Faires, Annette M. Burden
ISBN: 9781305253667

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Perform only two steps ofthe conjugate gradient method with C = C _1 == / on each ofthe