# Numerical Recipes Eq. 9.4.6!

by burnt
Tags: numerical, recipes
 P: 2 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 $$\epsilon$$ from the true root. Eq. 9.4.6: $$\epsilon_{i+1} = -\epsilon_i^2 \frac{f''(x)}{2f'(x)}$$ 2. Relevant equations Eq. 9.4.5: $$\epsilon_{i+1} = \epsilon_i + \frac{f(x_i)}{f'(x_i)}$$ $$\epsilon_i$$ represents deviation from true root. General Taylor expansion: Eq. 9.4.3: $$f(x+\epsilon) = f(x) + \epsilon f'(x) + ...$$ $$f'(x+\epsilon) = f'(x) + \epsilon f''(x) + ...$$ 3. The attempt at a solution $$\epsilon_{i+1} = \epsilon_i^2 \frac{f''(x)}{f'(x) + \epsilon_i f''(x)}$$ but this is not equation 9.4.6! Please help!

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