exception handling

[R. Baker Kearfott]

At 10:38 AM 3/16/96 -0800,  Douglas Priest wrote:


>[Hough]
>
>> Of course, most incorrect numerical results produced by programs are due 
>> source program bugs and optimizer bugs and incorrect input data, but aside
>> from those kinds of issues, the most common problem is roundoff.   But 
>> roundoff occurs during most programs deliver correct results, too, and there
>> isn't any way to distinguish good from bad except by human or automatic
>> analysis.     That's why interval methods are so important - they encompass
>> errors in the input data and its conversion to binary, in truncating analytic
>> processes to computational ones, in roundoff due to finite precision, AND
>> they handle underflow and overflow in a useful way as well.
>
>Interval methods don't "distinguish good [errors] from bad", they just
>provide bounds on errors from some sources.  Such methods are important
>because they are the only way to reliably solve problems that require
>global knowledge about functions.  They can be used to estimate the
>effects of errors and uncertainty in input data, though I would think
>that condition estimation would be a better way to do that.  Certainly
>there are much better ways than interval arithmetic to cope with roundoff.
>

I agree with your statement about reliably solving problems that require
global knowledge about functions.  IMHO interval methods are at their
best in that context.

Regarding your statement about interval methods and roundoff error,
I think it hinges on what you mean by "cope,"  and on the context
of the computation.  What other methods give you rigorous guarantees
that roundoff has been taken into account?  If logic dictates that 
number X should be in interval A, but the program produces an A
that does not contain X, then NECESSARILY there must be a 
bug in the program or malfunctioning hardware;  there is no ambiguity
about whether X is close enough to A.  This property of interval
arithmetic can be exploited in many contexts in properly laid-out
algorithms.
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R. Baker Kearfott,       rbkausl.edu      (318) 482-5346 (fax)
(318) 482-5270 (work)                     (318) 981-9744 (home)
URL: ftp://interval.usl.edu/pub/interval_math/www/kearfott.html
Department of Mathematics, University of Southwestern Louisiana
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