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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 zeroes (or roots) of a realvalued function. The algorithm is first in the class of Householder's methods, succeeded by Halley's method.
The NewtonRaphson method in one variable:
Given a function ƒ(x) and its derivative ƒ '(x), we begin with a first guess x_{0}. Provided the function is reasonably wellbehaved a better approximation x_{1} is
Geometrically, x_{1} is the intersection point of the tangent line to the graph of f, with the xaxis. The process is repeated until a sufficiently accurate value is reached:
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