Fr.: méthode de Newton-Raphson
A method for finding roots of a → polynomial that makes explicit use of the → derivative of the function. It uses → iteration to continually improve the accuracy of the estimated root. If f(x) has a → simple root near xn then a closer estimate to the root is xn + 1 where xn + 1 = xn - f(xn)/f'(xn). The iteration begins with an initial estimate of the root, x0, and continues to find x1, x2, . . . until a suitably accurate estimate of the position of the root is obtained. Also called → Newton's method.
→ Newton found the method in 1671, but it was not actually published until 1736; Joseph Raphson (1648-1715), English mathematician, independently published the method in 1690.