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    The answer to Fixed-point iteration

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    If the fixed-point iteration is applied to the function F(x) = 2 + (x-2)^4, starting at x = 2.5, what order of convergence results? Find the range of starting values for which this fixed-point iteration converges. Note that 2 is a fixed point.

    Please provide as much detail as possible so that I can understand how the solution is derived. I would like to understand this problem so that I can apply the techniques used to similar problems. I really appreciate your help!

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    Solution Preview

    Assume that is the root of the fixed point equation
    (1.1)
    In addition is continuously differentiable for all x near  and for some .
    Furthermore, assume that
    (1.2)
    Then if the initial guess is sufficiently close to , the iteration
    (1.3)
    Will ...

    Solution Summary

    Fixed-point iterations are analyzed.

    $2.19