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Re: Solving the system with inexact coefficients

• To: mathgroup at smc.vnet.net
• Subject: [mg99484] Re: [mg99335] Solving the system with inexact coefficients
• From: "Ted Ersek" <ersekt at md.metrocast.net>
• Date: Wed, 6 May 2009 05:28:14 -0400 (EDT)

A few people replied to a problem on how to find trancedental roots of a 
function in one dimension, and recommended my RootSearch package.

However, based on
http://blog.wolfram.com/2008/12/18/mathematica-7-johannes-kepler-and-transcendental-roots/#more-880

The built-in Root function is the prefeered approach in Mathematica 7 
(provided Root can handle the problem).
What trancedental roots can the Root function handle?
Well the above blog seems to indicate Root can find roots of a 
holomorphic function of a single variable.
The blog says a holomorphic function is essentially polynomials of 
infinite degree.

I say the built-in Root function is prefeered over RootSearch because 
the Root objects are tightly integrates into Mathematica. Also I believe 
the algorithms used by the Root function are gaurenteed to work 
(neglecting the effect of bugs). On the other hand my RootSearch package 
relies on taking a finite number of samples. RootSeach has been shown to 
be relaible, but it can be tricked by a pathological problem.

Notice the built-in Root function has been able to find the roots of a 
polynomial of any finite degree for a long time (those roots are 
algebraic numbers). More about the built-in Root function can be found 
at 
http://reference.wolfram.com/mathematica/ref/Root.html

My RootSeach function is still the method of choice for finding roots in 
one dimension when Root in Mathematica 7 can't be used.

Regards,

       Ted Ersek

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• Follow-Ups:
  • Re: Re: Solving the system with inexact coefficients
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>