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

Chapter 7, Problem 5

(choose chapter or problem)

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