Originally Posted by

**Mollier**

$\displaystyle \epsilon_{n+1} = \epsilon_n - \frac{f(\alpha+\epsilon_n)}{f'(\alpha+\epsilon_n)}$.

$\displaystyle

f(x)&=&f(\alpha+\epsilon_n) + f'(\alpha+\epsilon_n)(x-(\alpha+\epsilon_n)) + \frac{f ''(\alpha+\epsilon_n)}{2}(x-(\alpha+\epsilon_n))^2+ R \\

\end{aligned}

$.

I then let $\displaystyle x=\alpha$ and write it the Taylor series as,

$\displaystyle f(\alpha+\epsilon_n) = -f'(\alpha+\epsilon_n)\epsilon_n - \frac{f''(\alpha+\epsilon_n)}{2}\epsilon^2_n - R$.

I find $\displaystyle f'(x)$, let $\displaystyle x=\alpha$ and rewrite to get,

$\displaystyle f'(\alpha+\epsilon_n) = -f''(\alpha+\epsilon_n)\epsilon_n - R$.

If I substitute this into N-R, I do not get a reasonable answer. Where have I gone wrong?

Thanks.