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 --------------------------------------------------------------

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