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 ...".