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Re: [Help-gsl] Multiple roots

From: James Bergstra
Subject: Re: [Help-gsl] Multiple roots
Date: Sat, 15 Jul 2006 23:39:32 +0200
User-agent: Mutt/1.5.11+cvs20060403

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


For an example of general root-finding techniques, check out chapter 9
of numerical recipes:

The gsl's root-finding docs give a good intro to what various algos can
and cannot do:


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