Re: FindRoot on complex 'interval'
- To: mathgroup at smc.vnet.net
- Subject: [mg36948] Re: FindRoot on complex 'interval'
- From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
- Date: Thu, 3 Oct 2002 00:16:24 -0400 (EDT)
- Organization: Universitaet Leipzig
- References: <ane9j1$kgr$1@smc.vnet.net>
- Reply-to: kuska at informatik.uni-leipzig.de
- Sender: owner-wri-mathgroup at wolfram.com
Hi, and solving the real and imaginary part for for z->x+I*y with FindRoot[Evaluate[({Re[#] == 0, Im[#] == 0} &[ z^3 - 1]) /. z -> x + I y], {x, -3/2, 0}, {y, 0.5, 0.9}] helps not ? Regards Jens David J Strozzi wrote: > > 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.