On Convergence of the Secant Method

The secant method, as an important approach for solving nonlinear equations, is introduced in nearly all numerical analysis textbooks. However, most textbooks only briefly address the Q-order of convergence of this method, with few providing rigorous mathematical proofs. This paper establishes a rigorous proof for the Q-order of convergence of the secant method and theoretically compares its computational efficiency with that of Newton's method.