HW4 Solutions - Problem 6.1 Simple fixed-point iteration...

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Problem 6.1 Simple fixed-point iteration method Iteration x g(x) (i) ε (i)/ (i-1) ε ε 0 0.5 1.3 1 1.3 1.82 0.8 2 1.82 1.95 0.52 0.65 3 1.95 1.97 0.13 0.26 4 1.97 1.97 0.02 0.14 5 1.97 1.97 0 0.12 6 1.97 1.97 0 0.12 The ratio of errors approaches a c 7 1.97 1.97 0 0.12 which indicates the linear converg 8 1.97 1.97 0 0.12 f(x) = 2 sin( x) - x = 0 g(x) = x = 2 sin ( x)
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constant value, gence of the method.
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Problem 6.5 Newton-Raphson method Select which table to fill (1, 5): 5 Iteration x f(x) Iteration x f(x) 0 4.52 -11.69 0 4.54 -11.69 1 -807.21 ### 1 124.54 904479.55 2 -537.25 ### 2 83.94 267945.91 3 -357.28 ### 3 56.87 79358.89 4 -237.31 ### 4 38.85 23491.6 5 -157.33 ### 5 26.85 6945.22 6 -104.01 ### 6 18.89 2047.17 7 -68.47 ### 7 13.64 598.94 8 -44.79 -53200.89 8 10.23 171.85 9 -29.02 -15746.41 9 8.1 46.71 10 -18.53 -4654.8 10 6.9 10.79 11 -11.56 -1372.39 11 6.4 1.51 12 -6.97 -402.45 12 6.31 0.05 13 -3.96 -116.75 13 6.31 0 14 -2.04 -33.17 14 6.31 0 15 -0.86 -9.02 16 -0.19 -2.21 17 0.12 -0.4 18 0.21 -0.03 19 0.21 0 20 0.21
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HW4 Solutions - Problem 6.1 Simple fixed-point iteration...

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