What is called Newton’s method after Isaac Newton is an recursive procedure for computing approximations to zeros (“roots”) of differentiable functions with values in the real numbers.
Let $f \colon \mathbb{R} \to \mathbb{R}$ be a differentiable function and for $x_0 \in \mathbb{R}$ a real number such that the first derivative $f' \colon \mathbb{R} \to \mathbb{R}$ is non-vanishing at $x_0$.
Let $\{x_n \in \mathbb{R} | n \in \mathbb{N}\}$ be defined recursively by
Under mild conditions, this sequence converges to a zero/root of $f$.
Created on February 4, 2013 at 10:08:41. See the history of this page for a list of all contributions to it.