FindRoot can NOT handle mixed real and complex variables
- To: mathgroup at smc.vnet.net
- Subject: [mg79899] FindRoot can NOT handle mixed real and complex variables
- From: AES <siegman at stanford.edu>
- Date: Wed, 8 Aug 2007 04:53:08 -0400 (EDT)
- Organization: Stanford University
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 ]
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- From: Curtis Osterhoudt <cfo@lanl.gov>
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