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Re: Solve Limitations

• To: mathgroup at smc.vnet.net
• Subject: [mg63222] Re: Solve Limitations
• From: Paul Abbott <paul at physics.uwa.edu.au>
• Date: Mon, 19 Dec 2005 07:01:31 -0500 (EST)
• Organization: The University of Western Australia
• References: <IRGQVT$2C607F9DAA7468FE284C86E7560B5F2C@bol.com.br> <A67108E9-A365-40E5-856F-610C5E0BAEF1@mimuw.edu.pl> <200512140936.EAA02453@smc.vnet.net> <dnrcfl$khv$1@smc.vnet.net> <200512161222.HAA15821@smc.vnet.net> <do0lb9$415$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

In article <do0lb9$415$1 at smc.vnet.net>, Pratik Desai <pdesai1 at umbc.edu> 
wrote:

> >In article <dnrcfl$khv$1 at smc.vnet.net>, Pratik Desai <pdesai1 at umbc.edu> 
> >wrote:
> >
> >>To state the obvious, in general roots of analytic functions are hard to 
> >>find. I had the misfoutune to come across a nasty complex trancendental 
> >>equation. I found this Fortran Code ZEAL (Zeros of Analytic Functions) 
> >>quite invaluable. Needless to say, Solve, Reduce did not help much.
> >>http://cpc.cs.qub.ac.uk/summaries/ADKW_v1_0.html
> >>
> >>A Mathematica implimentation of this software would come a long way in 
> >>helping us poor engineers deal with such trancendental equations. The 
> >>system that I was dealing with has obvious practical significance, the 
> >>only hinderance being the lack of tools such as root solvers such as 
> >>ZEAL. Any takers??
> >>
> >>PS: Zeal not only can find the zeros of f(z) but also gives one the 
> >>values for f(z) with high degre of precision
> >
> >Have a look at the RootSearch package by Ted Ersek:
> >
> >  http://library.wolfram.com/infocenter/MathSource/4482/
> >
> >
> Thanks Paul
> I did try it out once. But I was under the impression it only dealt with 
> algebraics and reals, not analytic functions?

You are correct. In TMJ 6.1, Stan Wagon wrote a note about using 
ContourPlot to find the roots of two equations in two unknowns over a 
rectangular interval. This could be used to find the roots of analytic 
functions. See

  http://physics.uwa.edu.au/pub/Mathematica/MathGroup/RectangularRoots.nb

Cheers,
Paul

_______________________________________________________________________
Paul Abbott                                      Phone:  61 8 6488 2734
School of Physics, M013                            Fax: +61 8 6488 1014
The University of Western Australia         (CRICOS Provider No 00126G)    
AUSTRALIA                               http://physics.uwa.edu.au/~paul

• References:
  • Re: Re: Solve Limitations
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>
  • Re: Solve Limitations
    • From: Paul Abbott <paul@physics.uwa.edu.au>