Newton's method and high order iterations

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http://numbers.computation.free.fr/Constants/Algorithms/newton.html

Newton's method and high order iterations
Newton's method and high order iterations (Click here for a Postscript version of this page). 1 Introduction It is of great importance to solve equations of the form f(x)=0, in many applications in Mathematics, Physics, Chemistry, ... and of course in the computation of some important mathematical constants or functions like square roots. In this essay, we are only interested in one type of ...