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MathGroup Archive 1992

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Re: fateman?

  • To: mathgroup at yoda.physics.unc.edu
  • Subject: Re: fateman?
  • From: keiper
  • Date: Mon, 12 Oct 92 17:48:21 CDT

	> There's lots more wrong with RealInterval in Mathematica 2.0
	> (and I suspect in later versions).
	
Yes, there are problems with RealInterval[ ].  For example

In[2]:= RealInterval[{-2, 1}]^2

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

This particular bug has been fixed, but the fix will not appear until
the next version.

	> The concept of interval arithmetic in computational mathematics
	> requires that the result of an interval operation f on an
	> interval I includes every value f(a) where a is in I.

Yes, this idea is implemented in NumericalMath`IntervalAnalysis` and uses
rigorous, outward rounding to deal with inexact numbers.

	> Mathematica does not obey this rule.
	
All large computer programs have bugs.  Priorities must be set for fixing
them and until recently there was little indication that users were interested
in RealInterval[ ].  The recent interest expressed suggests that we need to
work harder on RealInterval[ ].

	> I suspect that this really is a consequence of its notion of
	> precision and accuracy,
	
This I very much doubt.  Rigorous, outward rounding is always possible.

	> plus some sloppiness in defining RealInterval. 

Agreed.

Jerry B. Keiper
keiper at wri.com






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