Re: [Help-gsl] Multiple roots

[James Bergstra]

On Sat, Jul 15, 2006 at 06:11:54PM +0000, Mohamed Ali Charmi wrote:
> Is it possible to find all the roots of a function

In general, this is difficult, and the answer is no.  Thinking about
your problem in particular might help... here are some quickly-generated
examples of questions that might be helpful to bear in mind if you are
considering a heuristic all-root-finding algo:

- Is there some general form of the functions you are interested in?  
- Do you know how many roots there are? 
- Do you know anything about where those roots are?  
- Is it possible to have double, triple roots?   
- Is the function continuous?  
- Is the function bounded by other functions that are easier to reason
  about?

------

For an example of general root-finding techniques, check out chapter 9
of numerical recipes:
http://www.library.cornell.edu/nr/cbookcpdf.html

The gsl's root-finding docs give a good intro to what various algos can
and cannot do:
http://www.gnu.org/software/gsl/manual/html_node/One-dimensional-Root_002dFinding.html#One-dimensional-Root_002dFinding

James
-- 
http://www-etud.iro.umontreal.ca/~bergstrj