Numerical method with convergence greater than 2 It is a well-known fact that, for solving algebraic equations, the bisection method has a linear rate of convergence, the secant method has a rate of convergence equal to 1.62 (approx.) and the Newton-Raphson method has a rate of convergence equal to 2.
Is there any numerical method for solving algebraic equations with a rate of convergence greater than 2?

In fact, one can go further. Joseph Traub has an entire book devoted to the construction of a family of methods that are effectively high-order generalizations of the Newton-Raphson and secant methods. On a more modern front, Bahman Kalantari constructed a "basic iteration" family that is a generalization of the Newton-Raphson and Halley methods. He also managed to produce some cool artwork in the process.
