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.

翻译：割线法作为求解非线性方程的一种重要方法，在几乎所有数值分析教材中均有介绍。然而，多数教材仅简要提及该方法的Q阶收敛性，鲜有给出严格的数学证明。本文建立了割线法Q阶收敛性的严格证明，并从理论上比较了其与牛顿法的计算效率。