RE: FindRoot on complex 'interval'
- To: mathgroup at smc.vnet.net
- Subject: [mg36978] RE: [mg36943] FindRoot on complex 'interval'
- From: "DrBob" <drbob at bigfoot.com>
- Date: Thu, 3 Oct 2002 05:33:33 -0400 (EDT)
- Reply-to: <drbob at bigfoot.com>
- Sender: owner-wri-mathgroup at wolfram.com
To the original function, add a function that's (a) zero when the
imaginary part is larger than some epsilon value you choose, (b) fairly
large when the imaginary part is 0 or negative, and (c) as smooth as
possible. For instance, something like:
f=Max[(1 - x/epsilon)^5, 0]
This function has four continuous derivatives in the real components --
though not in the complex variable!
If it doesn't penalize the real root enough, multiply f by a constant
bigger than 1 and try again.
From: David J Strozzi [mailto:dstrrozzi at MIT.EDU]
To: mathgroup at smc.vnet.net
Subject: [mg36978] [mg36943] FindRoot on complex 'interval'
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.
Prev by Date:
RE: Mathematica stole my X so I had to kill it
Next by Date:
Peculiar output from DSolve
Previous by thread:
Re: FindRoot on complex 'interval'
Next by thread:
Return["expr"] in functions and nested loops