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Everything about Secant method

Root-finding method

In numerical analysis, the secant method is a root-finding algorithm that uses a succession of roots of secant lines to better approximate a root of a function f. The secant method can be thought of as a finite-difference approximation of Newton's method, so it is considered a quasi-Newton method. Historically, it is as an evolution of the method of false position, which predates Newton's method by over 3000 years. Wikipedia →

🧭 Start here: a 6-step reading path

  1. Read the overview: Secant methodA 5-minute orientation
  2. Skim a recent paper: A three-term projection method based on spectral secant equation for nonlinear monotone equationsInfluential work since 2022
  3. Pick up a classic book: A treatise on ship-building and navigationThe most-reprinted book on the subject
  4. Read the landmark paper: The Secant method for simultaneous nonlinear equationsCited 133 times
  5. Go sideways: Muller's methodA closely related topic
  6. Go sideways: Steffensen's methodA closely related topic

📖 Definitions

Noun An iterative numerical method for finding a root of an equation f(x)=0, using a succession of roots of secant lines to better approximate the root.

🗂️ The subject at a glance

  1. The method
  2. Derivation of the method
  3. Convergence
  4. Comparison with other root-finding methods
  5. Practical considerations
  6. Generalization
  7. Example
  8. Algorithm

🏆 Landmark papers (most cited)

🆕 Influential since 2022

📚 Books worth reading

Ranked by number of editions on Open Library, a rough measure of how lasting a book is.

🔗 Related topics