The secant method of finding roots of nonlinear equations falls under the category of open methods. The secant method uses two initial guesses of the root but unlike the bisection method, they do not have to bracket the root.

Why is secant method considered open method?

In the secant method, it is not necessary that two starting points to be in opposite sign. Therefore, the secant method is not a kind of bracketing method but an open method.

Why is secant method faster than bisection?

Explanation: Secant method converges faster than Bisection method. Secant method has a convergence rate of 1.62 where as Bisection method almost converges linearly. Since there are 2 points considered in the Secant Method, it is also called 2-point method.