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Let f be a function f: R -> R and zeta a root of f, that is, f(zeta)=0. It is well known that if we take x_0 close to zeta, and under certain conditions that I will not explain here, the Newton method generates a sequence that converges to zeta. In fact, Newton's original ideas on the subject, around 1669, were cnsiderably more complicated. A systematic study and a simplified version of the method are due to Raphson in 1690, so this iteration scheme is also known as the Newton-Raphson method. (It has also been described as the tangent method, from its geometric interpretation.)
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