Fixed point iteration

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In numerical analysis, fixed point iteration is a method of computing fixed points of iterated functions.

More specifically, given a function f defined on the real numbers with real values and given a point x₀ in the domain of f, the fixed point iteration is X n+1= f (Xn), n = 0,1,2,... which gives rise to the sequence Xo, X1, X2,... which is hoped to converge to a point x. If f is continuous, then one can prove that the obtained x is a fixed point of f, i.e.,

f(x) = x

More generally, the function f can be defined on any metric space with values in that same space.

source: http://en.wikipedia.org/wiki/Fixed.Point.Iteration