[Edu-sig] "The study of fixed points has been at the foundation of algorithms"

[Arthur]

Scott David Daniels wrote:

>Well, in fact both meanings of "fixed point" are used, seldom by the
>same person.  I expect Knuth is in that small group that uses both
>meanings regularly (since his basic training was all mathematics).
>Look to the "functional programming" people for examination of the
>whole idea of fixed points of functions (Bird & Wadler is a standard
>F.P. text).
>  
>
thanks for the clarification as to terminology.

re:  "The study of fixed points has been at the foundation of algorithms"

I guess what I am asking further is whether the statement is simply 
referencing the development of  algorithms for solving the mathematical 
question of the fixed points of a function, in the context of 
mathematical programming where that particular mathematical problem 
might happen to present itself- or is there some implication that the 
problem of  f(x) = x is one that  has more general implications  in 
algorithmics as  a distinct area of study.

.. or am I asking a question that is itself too round-about to have an 
answer of the kind of am looking for? ;)

Art