Fixed-point iteration
Root-finding algorithm / From Wikipedia, the free encyclopedia
In numerical analysis, fixed-point iteration is a method of computing fixed points of a function.
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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.