On Convergence of the Secant Method
Numerical Analysis
2025-10-16 v1 Numerical Analysis
Abstract
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.
Keywords
Cite
@article{arxiv.2510.13228,
title = {On Convergence of the Secant Method},
author = {Yan Tan and Chenhao Ye and Qinghai Zhang and Shubo Zhao},
journal= {arXiv preprint arXiv:2510.13228},
year = {2025}
}