Numerical Recipes Eq. 9.4.6!

  1. 1. The problem statement, all variables and given/known data

    I want to derive equation Eq. 9.4.6 in Numerical Recipes from the expressions given, as stated in the book!
    The equation represents the next (i+1 th) deviation [tex]\epsilon[/tex] from the true root.
    Eq. 9.4.6:

    [tex]
    \epsilon_{i+1} = -\epsilon_i^2 \frac{f''(x)}{2f'(x)}
    [/tex]

    2. Relevant equations

    Eq. 9.4.5:

    [tex]
    \epsilon_{i+1} = \epsilon_i + \frac{f(x_i)}{f'(x_i)}
    [/tex]

    [tex]\epsilon_i[/tex] represents deviation from true root.


    General Taylor expansion:

    Eq. 9.4.3:
    [tex]
    f(x+\epsilon) = f(x) + \epsilon f'(x) + ...
    [/tex]

    [tex]
    f'(x+\epsilon) = f'(x) + \epsilon f''(x) + ...
    [/tex]



    3. The attempt at a solution

    [tex]
    \epsilon_{i+1} = \epsilon_i^2 \frac{f''(x)}{f'(x) + \epsilon_i f''(x)}
    [/tex]

    but this is not equation 9.4.6! Please help!
     
  2. jcsd
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