The Secant Method is second best to Newton’s Method, and is used when a faster convergence than Bisection is desired, but it is too difficult or impossible to take an analytical derivative of the func...The Secant Method is second best to Newton’s Method, and is used when a faster convergence than Bisection is desired, but it is too difficult or impossible to take an analytical derivative of the function \(f(x)\). \[f^{\prime}\left(x_{n}\right) \approx \frac{f\left(x_{n}\right)-f\left(x_{n-1}\right)}{x_{n}-x_{n-1}} \nonumber \] The interesting idea here is to determine which initial values of \(z_{0}\) in the complex plane converge to which of the three cubic roots of unity.
