Talk:Fixed-point iteration

What examples should be given in this article?

The Numerical analysis article gives one example of fixed point iteration: $x_{k+1}=(x_{k}^{2}-2)^{2}+x_{k}$ . This article can accommodate several examples and can illustrate them with graphics (maybe animations too?).

The example in the NA article can be complemented here by comparing it with the the superficially similar iteration: $x_{k+1}=(x_{k}^{2}-2)+x_{k}$ .

The Fixed point (mathematics) article has a nice graphic of an iteration of sin(x) that could be used to show that FPI can be used on many types of functions.

Examples of "what can go wrong" would also be nice.

Of course, examples are only part of the article.

--Jtir 14:13, 8 October 2006 (UTC)[reply]

I redirected this for now. Feel free to undo that if more example are added. Oleg Alexandrov (talk) 01:31, 9 October 2006 (UTC)[reply]

"fixed point iteration" is a technique in theoretical computer science

(copied from User talk:Oleg Alexandrov) --Jtir 06:17, 9 October 2006 (UTC)[reply]
Actually "fixed point iteration" is a technique in theoretical computer science: definition by recursion is regarded as solution of a fixed point problem g = F(g) and iterates of F converge to the fixed point. This technique has various flavors: an order theoretic one and a metric space one. --CSTAR 06:06, 9 October 2006 (UTC)[reply]