In numerical analysis, Newton's method, also known as the Newton–Raphson method, named after Isaac Newton and Joseph Raphson, is a root-finding algorithm which produces successively better See more

Newton's method is a powerful technique—in general the convergence is quadratic: as the method converges on the root, the difference … See more

Suppose that the function f has a zero at α, i.e., f(α) = 0, and f is differentiable in a neighborhood of α.
If f is continuously differentiable and its derivative is nonzero at α, then there exists a neighborhood of α such that for all starting values x0 … See more

Systems of equations
k variables, k functions
One may also use Newton's method to solve systems of k equations, which amounts to finding the (simultaneous) zeroes of k continuously differentiable functions See more

The idea is to start with an initial guess, then to approximate the function by its tangent line, and finally to compute the x-intercept of this tangent line. This x-intercept will typically be a better approximation to the original function's root than the first … See more

The name "Newton's method" is derived from Isaac Newton's description of a special case of the method in De analysi per aequationes numero terminorum infinitas (written … See more

Use of Newton's method to compute square roots
Newton's method is one of many known methods of computing square roots. Given a positive number a, the problem of finding a number x such that x = a is equivalent to finding a root of the … See more