Lesson plan
Halley's method
In numerical analysis, Halley's method is a root-finding algorithm used for functions of one real variable with a continuous second derivative. Edmond Halley was an English mathematician and astronomer who introduced the method now called by his name. The algorithm is second in the class of Householder's methods, after Newton's method. Like the latter, it iteratively produces a sequence of approximations to the root; their rate of convergence to the root is cubic. Multivariate versions of this method exist. Halley's method exactly finds the roots of a linear-over-linear Padé approximation to the function. This contrasts with Newton's method or the secant method, which approximate the function linearly, or Muller's method, which approximates the function quadratically. There is also Halley's irrational method, described below.
Article summary
In numerical analysis, Halley's method is a root-finding algorithm used for functions of one real variable with a continuous second derivative. Edmond Halley was an English mathematician and astronomer who introduced the method now called by his name. The algorithm is second in the class of Householder's methods, after Newton's method. Like the latter, it iteratively produces a sequence of approximations to the root; their rate of convergence to the root is cubic. Multivariate versions of this method exist. Halley's method exactly finds the roots of a linear-over-linear Padé approximation to the function. This contrasts with Newton's method or the secant method, which approximate the function linearly, or Muller's method, which approximates the function quadratically. There is also Halley's irrational method, described below.
Key claims
No claims recorded.
Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
Bibliography
No sources recorded.
Key claims and bibliography are generated from the same tracked claims and sources as the article page.