Editing Root-finding algorithm (section)

=== Newton's method (and similar derivative-based methods) ===
[[Newton's method]] assumes the function ''f'' to have a continuous [[derivative]]. Newton's method may not converge if started too far away from a root. However, when it does converge, it is faster than the bisection method; its [[order of convergence]] is usually quadratic whereas the bisection method's is linear. Newton's method is also important because it readily generalizes to higher-dimensional problems. [[Householder's method]]s are a class of Newton-like methods with higher orders of convergence. The first one after Newton's method is [[Halley's method]] with cubic order of convergence.