Joseph F. Newton

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 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