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
- References:
- Finding multiple roots
- From: "Novak Petrovic" <novak@itee.uq.edu.au>
- Finding multiple roots