Fixed-point computation

Fixed-point computation refers to the process of computing an exact or approximate fixed point of a given function. In its most common form, the given function ${\displaystyle f}$ satisfies the condition to the Brouwer fixed-point theorem: that is, ${\displaystyle f}$ is continuous and maps the unit d-cube to itself. The Brouwer fixed-point theorem guarantees that ${\displaystyle f}$ 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 various tasks, such as

• Nash equilibrium computation,
• Market equilibrium computation,
• Dynamic system analysis.