ON THE GENERALIZATION OF SECANT METHOD AND THE ORDER OF CONVERGENCE

In this paper we start generalizing the well known Secant and Müller methods by using higher degree polynomials. Although such generalization does already exist, we prove in an original and elegant way that the order of convergence $p$ is limited by p = 2. The techniques used in this paper could also be helpful in other contexts. We also perform some numerical experiments to reinforce the theoretical results.