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In numerical analysis, fixed-point iteration is a method of computing fixed points of a function.
More specifically, given a function defined on the real numbers with real values and given a point in the domain of , the fixed-point iteration is
which gives rise to the sequence of iterated function applications which is hoped to converge to a point . If is continuous, then one can prove that the obtained is a fixed point of , i.e.,More generally, the function can be defined on any metric space with values in that same space.