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

[FARKAS, Illes]

Sam, thanks for the reply. I set now each f_i to a large number whenever
its x_i is outside the [0,1] range, but still get the "iteration is not
making progress towards solution" error when starting with (0.1,0.1,0.1) or
(0.0,0.1,0.2). I suspect that I've made a very simple mistake somewhere :-)

The other method (below), with the embedded cubes, finds the solution.

Illes


2012/10/30 FARKAS, Illes <address@hidden>

> Thanks Juan,
>
> The equations are smooth (const, linear and quadratic terms on the
> r.h.s.), so the best I can come up with right now is to iterate with the
> following method.
>
> (A) Initialize cube size to (1,1,1) and cube center to (x1=0.5, x2=0.5,
> x3=0.5)
> (B) Compute the function (f1,f2,f3) in all equidistant 11 * 11 * 11 grid
> points of the cube
> (C) Find shortest (f1,f2,f3) vector and based on that decide if we're done
> (D) If we're not yet done, then:
>    - center cube on the (x1,x2,x3) location of the shortest (f1,f2,f3)
> vector
>    - reduce cube size to 60%
>    - goto (B)
>
> Do you think this makes sense?
>
> Thanks
> Illes
> --
> http://hal.elte.hu/fij
>
>
> 2012/10/30 Juan Pablo Amorocho <address@hidden>
>
>> 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
>>
>>
>
>
>
>
>


-- 
http://hal.elte.hu/fij