pythonic equivalent of Mathematica's FixedPoint function

[Terry Reedy]

"jelle" <jelleferinga at gmail.com> wrote in message 
news:1107335766.734539.281770 at l41g2000cwc.googlegroups.com...
> >You could probably write your own FixedPoint function without too much
>>difficulty, with the only tricky part being for it to know when to
> stop!
>
> It would be quite interesting to have this kind of function. But
> likely its far from trivial.

Fixed point iteration is a standard technique in numerical analysis --  
floating point calculations as approximation of real-number functions.  The 
first problem is getting an equation form that will converge  -- which has 
a stable, preferably unique fixed point.  The second is how to start --  
getting a first approximation that leads to convergence.  For stopping, one 
must choose between relative and absolute changes in the variable or 
expression (in x or y) or some combiniation thereof.

> FixedPoint seems to be one of the core functions in Mathematica, where
> many other functions are based on. Some additions such as FixedPoint
> would make functional programming in Python [easier].

It belongs in a module of floating-point equation solvers.  Perhaps one is 
already in scipy.

Terry J. Reedy