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Re: Re: How to View Mathematica and Hardcopy Books

• To: mathgroup at smc.vnet.net
• Subject: [mg62395] Re: [mg62374] Re: How to View Mathematica and Hardcopy Books
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Wed, 23 Nov 2005 01:12:10 -0500 (EST)
• References: <dls5ig$qn1$1@smc.vnet.net> <200511220942.EAA23713@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

On 22 Nov 2005, at 18:42, Steven T. Hatton wrote:

> For purposes of number crunching Mathematica is quite often the  
> wrong tool
> for the job.  If you are doing things which involve very intensive  
> mumeric
> calculation which are likely to be repeated in form, you are  
> probably much
> better off translating your work to something like C++, or  
> FORTRAN.  My
> understanding is that MathCode C++ can produce executables which  
> run orders
> of magnitude faster than the Mathematica implementation of the same
> algorithm


This is of course true in some cases. For example, if you are working  
on simulations in molecular biology then Mathematica would normally  
not be the right tool for the job. But the situation is quite  
different when what might be called "mathematical number crunching"  
is involved. First of all, the speed advantage of C++ usually  
disappears in cases when Mathematica has a built-in function that by  
itself does the job (and often the advantage lies with Mathematica  
since such functions tend to use the best known algorithms and are  
already highly optimised). But more importantly, in problems in  
numerical mathematics accuracy and the ability to keep track of  
errors is much more important than speed. There is no great advantage  
in getting a wrong answer several orders of magnitude faster.  
Mathematica offers pretty sophisticated tools that help with this  
task, which as far as I know no calculator does, nor is there, to my  
knowledge, anything comparable available in C++.

Andrzej Kozlowski

• References:
  • Re: How to View Mathematica and Hardcopy Books
    • From: "Steven T. Hatton" <hattons@globalsymmetry.com>