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FindRoot on complex 'interval'

• To: mathgroup at smc.vnet.net
• Subject: [mg36943] FindRoot on complex 'interval'
• From: David J Strozzi <dstrrozzi at MIT.EDU>
• Date: Wed, 2 Oct 2002 03:33:44 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

Hello,

I am trying to use FindRoot in mathematica 4.0 to find the zeros of a 
complex-valued function of one complex variable.  In particular, I am 
looking for the one root with a positive imaginary part.  I have a rough 
approximation for where the root should be, and this is good enough to 
give a reasonable guess.

However, there are always two other roots near the one I want - one with 
0 imaginary part and another with negative imag part.  (For those who 
are interested, the zeros are the roots of the dispersion relation for a 
plasma interacting with a laser).  Sometimes FindRoot picks up one of 
these instead of the one I want.

So, I'd like to tell mathematica to look for a root only in a certain 
rectangular region of the complex plane.  Well, if I could tell it, 
'look for roots with imag. part > something', I'd be happy too.

I tried specifying complex values for the start and stop points of an 
interval, hoping mathematica would interpret these as the corners of a 
rectangle.  No such luck.

Any help would be greatly appreciated.

I'd also like to point out that this and other issues about complex 
roots are not clearly addressed in the built-in help files.

Thanks much.

• Follow-Ups:
  • Re: FindRoot on complex 'interval'
    • From: Daniel Lichtblau <danl@wolfram.com>
  • Re: FindRoot on complex 'interval'
    • From: Selwyn Hollis <selwynh@earthlink.net>