HW4 Solutions

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

This preview shows pages 1–4. Sign up to view the full content.

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)

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
constant value, gence of the method.
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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 12

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

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online