I am an electrical engineer and don't have much background in numerical analysis. I am working on a problem which requires root-finding and many papers in the field refer to "Newton's method".
I found two "definitions" of this-
https://en.wikipedia.org/wiki/Newton%27s_method
https://en.wikipedia.org/wiki/Newton%27s_method_in_optimization
The first one uses the function and its first derivative while the second definition uses the first derivative and the second derivative during the iterations. So which of these are authors usually referring to when they talk about Newton's method?