Halley's method

Halley's method is a root-finding algorithm in numerical analysis for functions of one real variable that have a continuous second derivative. It was introduced by Edmond Halley, the English mathematician and astronomer whose name it carries. It is the second member of the class of Householder's methods, after Newton's method, and like Newton's method it iteratively produces a sequence of approximations to a root, but its rate of convergence is cubic. Where Newton's method and the secant method approximate the function linearly, Halley's method exactly finds the roots of a linear-over-linear Pade approximation to the function. Multivariate versions exist, and there is also a variant called Halley's irrational method.