Basin attractors for derivative-free methods to find simple roots of nonlinear equations - Beny Neta (Journal of Numerical Analysis and Approximation Theory, 2020)
Many methods exist for solving nonlinear equations. Several of these methods are derivative-free. One of the oldest is the secant method where the derivative is replaced by a divided difference. Clearly such method will need an additional starting value. Here we consider several derivative-free methods and compare them using the idea of basin of attraction.