Homotopy method
From Wikipedia, the free encyclopedia
Method for fixed-point computation
Not to be confused with Homotopy analysis method, a method for solving differential equations, devised in 1992 by Liao Shijun.
This article has multiple issues. Please help improve it or discuss these issues on the talk page . (Learn how and when to remove these messages)
(Learn how and when to remove this message)The topic of this article may not meet Wikipedia's general notability guideline . Please help to demonstrate the notability of the topic by citing reliable secondary sources that are independent of the topic and provide significant coverage of it beyond a mere trivial mention. If notability cannot be shown, the article is likely to be merged, redirected, or deleted.
Find sources: "Homotopy method" – news · newspapers · books · scholar · JSTOR (August 2025) (Learn how and when to remove this message)
Find sources: "Homotopy method" – news · newspapers · books · scholar · JSTOR (August 2025) (Learn how and when to remove this message)
This article needs to be updated. Please help update this article to reflect recent events or newly available information. (August 2025)
The homotopy method is a method for fixed-point computation, based on the mathematical concept of homotopy. The method was devised in 1972 by B. Curtis Eaves.[1]
Given a function f, for which we want to find a fixed point, the algorithm works by starting with an affine function that approximates f, and deforming it towards f while following the fixed point.
Applications
[edit ]The homotopy method has been used for market equilibrium computation.[2]
Further reading
[edit ]The method is further explained in a book by Michael Todd,[3] which surveys various algorithms developed until 1976.
References
[edit ]- ^ Eaves, B. Curtis (December 1972). "Homotopies for computation of fixed points". Mathematical Programming. 3–3 (1): 1–22. doi:10.1007/BF01584975. S2CID 39504380.
- ^ Codenotti, Bruno; Pemmaraju, Sriram; Varadarajan, Kasturi (2004年12月01日). "The computation of market equilibria" . SIGACT News. 35 (4): 23–37. doi:10.1145/1054916.1054927. ISSN 0163-5700.
- ^ The Computation of Fixed Points and Applications. Lecture Notes in Economics and Mathematical Systems. Vol. 124. 1976. doi:10.1007/978-3-642-50327-6. ISBN 978-3-540-07685-8.
Stub icon
This algorithms or data structures-related article is a stub. You can help Wikipedia by expanding it.