[4] Computational exercise Consider the nonlinear svstem in (31.
(a) Apply the fixed-point iteration with 20) = (0.5. 0.3)7 to approximate
the fixed point. Iterate until |(2() – pIlo < 10-7. (The fixed point is p
(v3/2, 1/2)T)
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(b) What is the actual number of iterations needed to reach the accuracy
10-7 in fo norm. Why this number is smaller than the one you obtained in
(c) Apply the Gauss-Seidel fixed-point iteration with #0) = (0.5. 0.3) T to
approximate the fixed point. Iterate until ||24) – pilo. < 10-7
[5 Computational exercise Use Newton's met hod to find a solution(approximate
solution) to the following nonlinear systems. Iterate until |2() - a-D)Il
Use 20) = (1.1)7
- cos(I2.23)
2? - 62523
e-7172 + 2022 +
Use 20) = (1.1. -1)T. This Newton's iteration may converge slow, comment
on this slow convergence.
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