Is Newton's Method to compute the zeros of a function an algorithm? Looking for Newton's method in Wikipedia, I read the following:


  In numerical analysis, Newton's method (also known as the
  Newton-Raphson method), named after Isaac Newton and Joseph Raphson,
  is a method for finding successively better approximations to the
  roots (or zeroes) of a real-valued function.


After describing briefly the method, the Wikipedia page adds:


  This algorithm is first in the class of Householder's methods,
  succeeded by Halley's method. The method can also be extended to
  complex functions and to systems of equations.


The emphasis on "algorithm" is mine.

I know Wikipedia is not always to be trusted, and I have been
wondering whether Newton's method as described in Wikipedia does
qualify as an algorithm, and what could be the reasons why it would
qualify or not qualify.

The same question applies to other similar methods, such as the whole
family of Householder's methods, also described in Wikipedia, but an
answer in the Newton-Raphson case is enough.

Note, as a last remark, that the same question could be applied to Euclid's method to compute GCD as described in Wikipedia, though I expect the answer would be: "yes, because ...".

Related questions:


What exactly is an algorithm?
Do Turing machines assume something infinite at some point?
It's pretty clearly an algorithm according to my definition in the linked question. I think your real question is "what is the problem, if any, for which this algorithm is correct?" The answer would be something like "given some stuff and a number of iterations, output a value satisfying some condition with an accuracy related to the iteration count."