Newton's method

Named after Isaac Newton.

Newton's method

1. (algebra, calculus) A method for finding successively better approximations to the roots (or zeroes) of a real-valued function.

For the equation ${\displaystyle f(x)=0}$, the iteration is ${\displaystyle x_{n+1}=x_{n}-{\frac {f(x_{n})}{f'(x_{n})}}}$, where ${\displaystyle n=0,1,2,...}$, and ${\displaystyle x_{0}}$ is the first approximation to the solution.

• Newton-Raphson method