Fixed-point computation: Difference between revisions

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{{Short description|Computing the fixed point of a function}}

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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">{{cite book |doi=10.1007/978-3-642-50327-6 |title=The Computation of Fixed Points and Applications |series=Lecture Notes in Economics and Mathematical Systems |year=1976 |volume=124 |isbn=978-3-540-07685-8 }}</ref> In its most common form, the given function <math>f</math> satisfies the condition to the [[Brouwer fixed-point theorem]]: that is:, <math>f</math> is continuous and maps the unit [[N-cube|''d''-cube]] to itself. The [[Brouwer fixed-point theorem]] guarantees that <math>f</math> has a fixed point, but the proof is not [[Constructive proof|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 ==