[SciPy-user] zeros of a function

[lorenzo bolla]

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
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.


On 5/23/07, Anne Archibald <peridot.faceted at gmail.com> wrote:
>
> On 23/05/07, william ratcliff <william.ratcliff at gmail.com> wrote:
> > What about re-expressing the problem as a nonlinear optimization problem
> > where you're fitting a function function to a vector of zeros?  Then,
> use
> > your favorite global optimizer to try to find the minima of the "chi^2"
> of
> > this function.  The issue here is that for some functions, even a global
> > optimizer could run into problems...
>
> Global optimization is *hard*. If you make a scalar function by (say)
> computing the squared length of a vector you want to find a zero of,
> you're almost certain to wind up with zillions of spurious local
> minima. They talk about this in Numerical Recipes too.
>
> Anne
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