Re: [Help-gsl] solution of 3d quadratic algebraic system

[Juan Pablo Amorocho]

Hi Illes,
As far as I know, you can't tell Newton to stay within a "region of interest" ( 
@help-gnu If I'm wrong please correct me). All you can do is to provide the 
solver with a reasonable starting point. You could also take a look at your 
function around that region of interest, and see if it behaves nasty.  Maybe 
this could help:

http://en.wikipedia.org/wiki/Newton_iteration#Practical_considerations 

- Juan Pablo
 
On Oct 30, 2012, at 6:40 AM, "FARKAS, Illes" <address@hidden> wrote:

> 2012/10/29 FARKAS, Illes <address@hidden>
> 
>> 2012/10/28 Rhys Ulerich <address@hidden>
>> 
>>>> Can you please suggest a fast GSL method / algorithm to find the
>>> solutions
>>>> of a quadratic 3d system of algebraic equations?
>>>> 
>>>> In the reduced form all 3 equations have zero on the l.h.s., and on the
>>>> r.h.s. there are constant, linear and quadratic terms composed of x1,
>>> x2,
>>>> x3 (the three variables).
>>> 
>>> Newton iteration, especially if you provide analytic Jacobian, should do
>>> well here. There may be faster things that can return multiple solutions,
>>> however.
>>> 
>>> - Rhys
>>> 
>> 
>> Thanks, I've chosen the hybrid 
>> algorithm<http://www.gnu.org/software/gsl/manual/html_node/Example-programs-for-Multidimensional-Root-finding.html>
>> .
> 
> 
> Hello,
> 
> The 3 variables represent biochemical concentrations normalized to the
> interval [0,1]. Can I tell the solver (or another solver) that it should
> stay inside this interval? I keep receiving solutions outside this
> interval, which are mathematically OK, but biochemically really nonsense.
> Also, with some help I'm ready to read/write the source code.
> 
> Many thanks!
> 
> Illes