Source : Free On-Line Dictionary of Computing

Newton-Raphson
     
        A well-known {algorithm} for solving equations.  Given an
        equation,
     
        	f x = 0
     
        and an initial approximation, x(0), a better approximation is
        given by:
     
        	x(i+1) = x(i) - f(x(i)) / f'(x(i))
     
        where f'(x) is the first derivative of f, df/dx.