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MathGroup Archive 2004

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numbers near machine precision

  • To: mathgroup at smc.vnet.net
  • Subject: [mg47049] numbers near machine precision
  • From: Steve Story <sbstory at ncsu.edu>
  • Date: Mon, 22 Mar 2004 00:15:01 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

I'm in a numerical methods class, and having difficulty adapting the 
subroutines to Mathematica. For one thing, it seems that the == operator 
will pronounce two numbers equal when they're much further apart than 
machine epsilon.

And I don't understand why this is, but it's easy to work around for the 
routines I'm using. A bigger problem, however, is that when I try to 
look at a machine-precise number in different number systems, sometimes 
Mathematica says they're identical, sometimes not. And I can't find a 
good resource about this. This problem is much more confusing to me. 
Here's an example which I can't explain. In the first case, they're not 
identical, in the second, they are:

In[132]:=
RealDigits[{a,b},2]

Out[132]=
{{{1,0,0,1,0,0,0,1,1,0,1,1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0,0,1,1,1,1,1,1,1,0,
 
1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0},2},{{1,0,0,1,0,0,0,1,1,0,1,1,1,1,1,0,1,
 
0,0,1,0,1,0,0,1,0,1,0,0,1,1,1,1,1,1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,
     1},2}}

In[135]:=
RealDigits[{a,b},16]

Out[135]=
{{{2,4,6,15,10,5,2,9,15,13,11,3,3},1},{{2,4,6,15,10,5,2,9,15,13,11,3,3},1}}

I don't understand why those things are happening in Mathematica. If anyone 
could point me to a deep discussion of these topics in Mathematica, I'd 
appreciate it.

thanks,
Steve Story


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