Newton's method

Algorithm for finding zeros of functions

In numerical analysis, the Newton–Raphson method, also known simply as Newton's method, named after Isaac Newton and Joseph Raphson, is a root-finding algorithm which produces successively better approximations to the roots (or zeroes) of a real-valued function. The most basic version starts with a real-valued function f, its derivative f′, and an initial guess x0 for a root of f. If f satisfies certain assumptions and the initial guess is close, then x 1 = x 0 − f ( x 0) f ′ ( x 0) {\displaystyle x_{1}=x_{0}-{\frac {f(x_{0})}{f'(x_{0})}}} is a better approximation of the root than x0.

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