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Re: Finding multiple roots

  • To: mathgroup at smc.vnet.net
  • Subject: [mg38279] Re: [mg38225] Finding multiple roots
  • From: Daniel Lichtblau <danl at wolfram.com>
  • Date: Tue, 10 Dec 2002 04:17:35 -0500 (EST)
  • References: <200212050836.DAA04089@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Novak Petrovic wrote:
> 
> Hi all,
> 
> I'm trying to find roots of the characteristic equation of a
> dielectric-loaded waveguide. There are multiple roots of the equation and I
> use FindRoot to find them. The sequence of roots is very important in my
> further calculations.
> 
> Is there a routine or a clever way to (numerically) find all the roots of an
> equation in a predefined values?
> 
> As it is now I have to look for each individual root manually and it gets a
> bit tedious as the number of required modes increases.
> 
> Thanks a lot.
> 
> --
> Regards,
> 
> Novak Petrovic
> novak at itee.uq.edu.au

This probably depends on the specifics of your equations (polynomial?
exponential? analytic? other?) and region of interest (a segment?
rectangle in complex plane? something else?). A similar question was
raised at the URL below. Several replies showed various approaches one
might take.

http://forums.wolfram.com/mathgroup/archive/2001/Jun/msg00226.html

For certain special cases one might be able to get exact solutions e.g.
by using Solve and taking advantage of periodicity e.g. for a
trigonometric polynomial. This can only be done if the equation is such
that Solve can form a polynomial in some reasonable set of "variables".

Daniel Lichtblau
Wolfram Research


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