On Convergence of the Secant Method
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866914094030782464 |
|---|---|
| author | Tan, Yan Ye, Chenhao Zhang, Qinghai Zhao, Shubo |
| author_facet | Tan, Yan Ye, Chenhao Zhang, Qinghai Zhao, Shubo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_13228 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Convergence of the Secant Method Tan, Yan Ye, Chenhao Zhang, Qinghai Zhao, Shubo Numerical Analysis 41A25, 68W40 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. |
| title | On Convergence of the Secant Method |
| topic | Numerical Analysis 41A25, 68W40 |
| url | https://arxiv.org/abs/2510.13228 |