Re: FindRoot can NOT handle mixed real and complex variables

*To*: mathgroup at smc.vnet.net*Subject*: [mg79938] Re: [mg79899] FindRoot can NOT handle mixed real and complex variables*From*: Curtis Osterhoudt <cfo at lanl.gov>*Date*: Thu, 9 Aug 2007 05:19:29 -0400 (EDT)*References*: <200708080853.EAA05884@smc.vnet.net>*Reply-to*: cfo at lanl.gov

I may be misunderstanding what you want. At least with $Version "6.0 for Linux x86 (32-bit) (June 19, 2007)" the following works, though it homes in on the same roots for every (tested) starting value of "DN" between -10^6 and +10^6: solns = ({#1, FindRoot[{u*BesselJ[1, u]*BesselK[0, w] == w*BesselK[1, w]*BesselJ[0, u], u^2 + w^2 == g, Re[g] == input\[Breve]value, Re[w] == 0}, {{u, -2.39 + 0.17*I}, {w, 14.34*I}, {g, -200 + 0.8*I}, {input\[Breve]value, #1}}]} & ) /@ Range[-10^6, 10^6, 10^4] Perhaps things will converge to different root values for radically different starting values, but this seems to handle the system adequately. On Wednesday 08 August 2007 02:53:08 AES wrote: > I'm (re)posting this as an assertion, not a question, hoping to rouse a > little more interest, since it appears to be a significant weakness in > FindRoot, and a previous post, rather unusually, brought no satisfactory > resolution; > > The problem is to find the roots of two complex equations > > u * BesselJ[1, u] * BesselK[0, w] == w * BesselK[1, w] * BesselJ[0, u] > > u^2 + w^2 == g > > with constraints > > Re[g] == <an input value, DN> > > Re[w] == 0 > > So that's two complex (or four real) equations; four real numbers in the > desired output; and at least one solution exists in general for any > choice of DN and can be found using other methods -- but there appears > to be NO WAY (no straightforward way, anyway) to find it using FindRoot, > -- or even to get FindRoot to tackle the basic problem. > > Right???????? > > ------ > > [For testing purposes, a sample starting point close to but not exactly > one particular solution, would be DN = -200, g0 = DN + 0.8 I = -200 + > 0.8 I, u0 = 2.39 + 0.17 I, w0 = 0 + 14.34 I ] -- ========================================================== Curtis Osterhoudt cfo at remove_this.lanl.and_this.gov PGP Key ID: 0x4DCA2A10 Please avoid sending me Word or PowerPoint attachments See http://www.gnu.org/philosophy/no-word-attachments.html ==========================================================

**References**:**FindRoot can NOT handle mixed real and complex variables***From:*AES <siegman@stanford.edu>