I understand the algorithms and the formulae associated with numerical methods of finding roots of functions in the real domain, such as Newton's Method, the Bisection Method, and the Secant Method. Because their formulae are constructed differently, innately they will differ numerically at certain iterations. However, what are the exact advantages of each one algorithm.
All I know about these algorithms, other than their formualae are:
Newton's Method converges quadrilaterally
Secant Method bypasses the need to compute a derivative, however converges superlinearly.
Bisection method converges linearly