Newton-Raphson iteration

from The Free On-line Dictionary of Computing (8 July 2008)

Newton-Raphson iteration

   <algorithm> An iterative {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.

   Newton-Raphson iteration is an example of an {anytime
   algorithm} in that each approximation is no worse than the
   previous one.

   (2007-06-19)