[SciPy-user] zeros of a function

[Nils Wagner]

lorenzo bolla wrote:
> Thanks to all for the replies.
> Following Emanuele's suggestion and googling for the problem, I came
> up with this:
> http://interval.sourceforge.net/interval/prolog/clip/clip/smath/README.html
> <http://interval.sourceforge.net/interval/prolog/clip/clip/smath/README.html>
> It's a library doing interval arithmetics (more info here:
> http://www.cs.utep.edu/interval-comp/)
> <http://www.cs.utep.edu/interval-comp/>.
> Basically, one can scan for zeros of a function f, whose analytical
> formula is known, in an interval by bisectioning the interval itself
> and evaluating the function with the interval arithmetics formulas.
>  
> the fundamental property of interval arithmetics is this:
> let y=f(x) be the function, one can define [c,d] = f([a,b]), with
> [a,b] and [c,d] intervals, so that for every x in [a,b]: f(x) is in [c,d].
>  
> i.e.: in interval arithmetics: sin([0,pi]) = [0,1]
>  
> then bisect the interval and exclude all the intervals where [c,d]
> does not contain zero. keep on bisecting till machine precision :-)
> this procedure assure to find ALL the zeros.
> comments?
>  
> L.
>
PyDX is a package for working with interval arithmetic.

 http://gr.anu.edu.au/svn/people/sdburton/pydx/doc/user-guide.html#interval-arithmetic
 
Nils