Question

In Newton-Raphson's method, what is the formula, after first iteration.

Answer 1

Newton-Raphson's method,

$x_{n+1}=x_n-\frac{f\left(x_n\right)}{f^{\prime }\left(x_n\right)}$

$x_1=x_0-\frac{f\left(x_0\right)}{f^{\prime }\left(x_0\right)}$

After first iteration,

$x_2=x_1-\frac{f\left(x_1\right)}{f^{\prime }\left(x_1\right)}$

$x_2=[x_0-\frac{f\left(x_0\right)}{f^{\prime }\left(x_0\right)}]-\frac{f\left(x_1\right)}{f^{\prime }\left(x_1\right)}$

$x_{n+1}=x_{n-1}-\frac{f\left(x_{n-1}\right)}{f^{\prime }\left(x_{n-1}\right)}-\frac{f\left(x_n\right)}{f^{\prime }\left(x_n\right)}$

$x_{n+1}=x_{n-1}-\left[\frac{f\left(x_{n-1}\right)f^{\prime }{(x}_n)-f{(x}_n)f^{\prime }\left(x_{n-1}\right)}{f^{\prime }\left(x_{n-1}\right)f^{\prime }{(x}_n)}\right]$