Fixed-point iteration
Root-finding algorithm / From Wikipedia, the free encyclopedia
Dear Wikiwand AI, let's keep it short by simply answering these key questions:
Can you list the top facts and stats about Fixed-point iteration?
Summarize this article for a 10 year old
SHOW ALL QUESTIONS
In numerical analysis, fixed-point iteration is a method of computing fixed points of a function.
This article needs additional citations for verification. (May 2010) |
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.