Newton-Raphson or Newton's Method

It is a type of Banach’s iteration

Mathematically

We assume that there is a fixed point $k$ in the domain of $x$ such that

$$g(x_k)=x_k$$

The general iteration formula

$$\begin{array}{rl}& g(x_{k+1})=x_{k+1}=x_k-\lambda \cdot \frac{f(x_k)}{D}\end{array}$$

$\text{ e.g. }\lambda =1,D=\nabla f\left(x_k\right)$

$$g(x_{k+1})=x_k-\frac{f(x_k)}{f^{\prime }(x_k)}$$