fixed point

A value p where a function g leaves its input unchanged: g(p) = p.

A fixed point of a function $g$ is a value $p$ with $g(p) = p$ . Rearranging a root-finding equation $f(x)=0$ into the form $x = g(x)$ turns the search for a root of $f$ into a search for a fixed point of $g$ , computed by the iteration $x_{n+1} = g(x_n)$ .

Examples

$g(x)=\cos x$ has a fixed point near $p\approx0.739$ , since $\cos(0.739)\approx0.739$ .