Re: Re: Equation - problem

*To*: mathgroup at smc.vnet.net*Subject*: [mg49006] Re: [mg48993] Re: [mg48981] Equation - problem*From*: "Janos D. Pinter" <jdpinter at hfx.eastlink.ca>*Date*: Mon, 28 Jun 2004 04:13:51 -0400 (EDT)*References*: <200406252152.RAA21757@smc.vnet.net> <200406260555.BAA26730@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

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. Adjunct Professor, Dalhousie University 129 Glenforest Drive, Halifax, NS, Canada B3M 1J2 Telephone: +1-(902)-443-5910 Fax: +1-(902)-431-5100; +1-(902)-443-5910 E-mail: jdpinter at hfx.eastlink.ca 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/

**References**:**Equation - problem***From:*"RAFAL" <rak@dami-rz.pl>

**Re: Equation - problem***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>