Re: Re: Equation - problem

```Colleagues,

This problem (as well as many similar ones) may have multiple solutions, as
stated in my earlier comment on nonlinear eqns.

Here is another solution, calculated using l2-norm in the error (objective)
function and applying MathOptimizer Professional:

{x -> 0.7446861199, q -> 3.7724953212, r -> 1.4900166563}; the
corresponding l2-error is 9.046868354683253 x 10^-23.

Regards,
Janos
_________________________________________________

Janos D. Pinter, PhD, DSc
President & Research Scientist, PCS Inc.

129 Glenforest Drive, Halifax, NS, Canada B3M 1J2
Telephone: +1-(902)-443-5910
Fax: +1-(902)-431-5100; +1-(902)-443-5910
Web: www.dal.ca/~jdpinter   www.pinterconsulting.com

At 02:55 AM 6/26/2004, you wrote:
>On 26 Jun 2004, at 06:52, RAFAL wrote:
>
> > Hi
> >
> > I need a good package for computing the equation like below:
> >
> > Reduce[r^2*(x^q - 1)*(( - r*x*(x^q - 1 ))^q - 1) == 1 && r >= 0 &&
> > 0 <= x <= 1 && q > 0, x, Reals]
> >
> > Thanks
> >
> > rak
> >
>If you mean that you want to compute x as an explicit function of r and
>q, than not only does no software for this exists know, but almost
>certainly will never exist in the future either.
>
>If, on the other hand, all you want is to find a triple of reals x,q,r
>that approximately satisfy the equation than Mathematica can do it
>quite easily:
>
>
>Chop[NMinimize[
>     {Abs[r^2*(x^q - 1)*(((-r)*x*(x^q - 1))^q - 1) - 1],
>      0 <= r <= 10 && 0 <= x <= 1 && 0 <= q <= 10},
>     {x, r, q}]]
>
>{0, {q -> 0.3562694885703915, r -> 7.731875654183964,
>     x -> 0.6779077010660948}}
>
>
>Andrzej Kozlowski
>Chiba, Japan
>http://www.mimuw.edu.pl/~akoz/

```

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