       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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