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Numerical Recipes Eq. 9.4.6! 
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#1
Sep2210, 02:54 PM

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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! 


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