Solved: Use Theorem 10.6 to show that G : D R3 R3 has a unique fixed point in D. Apply

Chapter 10, Problem 7

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Use Theorem 10.6 to show that G : D R3 R3 has a unique fixed point in D. Apply functional iteration to approximate the solution to within 105, using the l norm. a. G(x1, x2, x3) = cos(x2x3) + 0.5 3 , 1 25 x2 1 + 0.3125 0.03, 1 20 ex1x2 10 3 60 t ; D = {(x1, x2, x3)t | 1 xi 1, i = 1, 2, 3 } b. G(x1, x2, x3) = 13 x2 2 + 4x3 15 , 11 + x3 x2 1 10 , 22 + x3 2 25 ; D = {(x1, x2, x3)t | 0 x1 1.5, i = 1, 2, 3 } c. G(x1, x2, x3) = (1 cos(x1x2x3), 1 (1 x1)1/4 0.05x2 3 + 0.15x3, x2 1 + 0.1x2 2 0.01x2 + 1)t ; D = {(x1, x2, x3)t | 0.1 x1 0.1, 0.1 x2 0.3, 0.5 x3 1.1 } d. G(x1, x2, x3) = 1 3 cos(x2x3) + 1 6 , 1 9 x2 1 + sin x3 + 1.06 0.1, 1 20 ex1x2 10 3 60 t ; D = {(x1, x2, x3)t | 1 xi 1, i = 1, 2, 3 } Copy