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Everything about Root-finding algorithm

Algorithms for zeros of functions

In numerical analysis, a root-finding algorithm is an algorithm for finding zeros, also called roots, of a function. A root of the function f is a number x such that f(x) = 0. As the zeros typically cannot be computed exactly, nor expressed in closed form, root-finding algorithms provide approximations to the zeros. The functions considered are typically continuous or, for most algorithms, differentiable. For real functions and complex functions, the approximations are commonly expressed as floating-point numbers, sometimes with error bounds. Wikipedia →

🧭 Start here: a 6-step reading path

  1. Read the overview: Root-finding algorithmA 5-minute orientation
  2. Skim a recent paper: A Novel Root-Finding Algorithm With Engineering Applications and its Dynamics via Computer TechnologyInfluential work since 2022
  3. Pick up a classic book: An introduction to computer scienceThe most-reprinted book on the subject
  4. Read the landmark paper: The root-MUSIC algorithm for direction finding with interpolated arraysCited 221 times
  5. Go sideways: Newton's methodA closely related topic
  6. Go sideways: Polynomial root-findingA closely related topic

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🗂️ The subject at a glance

  1. Bracketing methods
  2. Interpolation
  3. Iterative methods
  4. Combinations of methods
  5. Roots of polynomials
  6. Finding roots in higher dimensions

🏆 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