Fixed-point computation: Difference between revisions

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'''Fixed-point computation''' refers to the process of computing an exact or approximate [[Fixed point (mathematics)|fixed point]] of a given function.<ref name=":1">{{Citecite bookjournal |urldoi=https://link.springer.com/book/10.1007/978-3-642-50327-6 |title=The Computation of Fixed Points and Applications |language=en |doi=10.1007/978-3-642-50327-6}}{{pn}}</ref> In its most common form, we are given a function ''f'' that satisfies the condition to the [[Brouwer fixed-point theorem]], that is: ''f'' is continuous and maps the unit [[N-cube|''d''-cube]] to itself. The [[Brouwer fixed-point theorem]] guarantees that ''f'' has a fixed point, but the proof is not constructive. Various algorithms have been devised for computing an approximate fixed point. Such algorithms are used in economics for computing a [[market equilibrium]], in game theory for computing a [[Nash equilibrium]], and in [[dynamic system]] analysis.
 
== Definitions ==