Examples of when Newton's Method will fail? Newton's method eventually gets into the never ending cycle, bouncing between the same two approximations x_i and x_(i)+1.

Luciano Webster 2022-07-22 Answered
Examples of when Newton's Method will fail?
Newton's method eventually gets into the never ending cycle, bouncing between the same two approximations x i and x i + 1 .
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Answers (1)

suponeriq
Answered 2022-07-23 Author has 10 answers
f ( x ) = { x , x 0 x , x < 0
has the peculiar property that for any initial guess x 0 0, the orbit is trapped in a cycle of period 2, with x k = x k 1 . This is quite easy to prove and is left as an exercise for the reader.
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