linguistic:paraphrasing, structural:expansion
Fixed point iteration

In numerical analysis, fixed-point iteration is a method of computing fixed points of a function. Specifically, given a function f {\displaystyle f} with the same domain and codomain, a point x 0 {\displaystyle x_{0}} in the domain of f {\displaystyle f}, the fixed-point iteration is

x n + 1 = f (x n), n = 0, 1, 2, … {\displaystyle x_{n+1}=f(x_{n}),\,n=0,1,2,\dots }

which gives rise to the sequence x 0, x 1, x 2, … {\displaystyle x_{0},x_{1},x_{2},\dots } of iterated function applications x 0, f (x 0), f (f (x 0)), … {\displaystyle x_{0},f(x_{0}),f(f(x_{0})),\dots } which is hoped to converge to a point x {\displaystyle x}. If f {\displaystyle f} is continuous, then one can prove that the obtained x {\displaystyle x} is a fixed point of f {\displaystyle f}.

The notions of attracting fixed points, repelling fixed points, and periodic points are defined with respect to fixed-point iteration.