In numerical analysis, Newton’s method (also known as the Newton–Raphson method), named after Isaac Newton and Joseph Raphson, is a method for finding successively better approximations to the roots (or zeroes) of a real-valued function.
x : f(x) = 0 .
The Newton–Raphson method in one variable is implemented as follows:
Given a function ƒ defined over the reals x, and its derivative ƒ’, we begin with a first guess x0 for a root of the function f. Provided the function satisfies all the assumptions made in the derivation of the formula, a better approximation x1 is
x_1 = x_0 - .
Geometrically, (x1, 0) is the intersection with the x-axis of the tangent to the graph of f at (x0, f (x0)).
The process is repeated as
until a sufficiently accurate value is reached.