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From: rh@craycos.com (Robert Herndon)
Newsgroups: comp.arch
Subject: Re: Implementing Interval Arithmetic with IEEE rounding modes
Message-ID: <1991Jun18.224526.6449@craycos.com>
Date: 18 Jun 91 22:45:26 GMT
Organization: Cray Computer Corporation
Lines: 28

While I've seen lots of verbage on the pros and cons of interval
operations, I've seen NO discussion of its impact on algorithms.
The question is then, how does one allow for changes of algorithm
flow because of interval arithmetic?  I.e., any time a decision
is made based on the value of an interval, one sees a dichotomy
of possible flow paths.

E.g., partial pivoting requires selection of the largest element of 
a matrix column.  If interval arithmetic shows that two elements'
intervals overlap, how does one choose?  Presumably, one picks the
element with the larger potential absolute value, but this may be
a bad choice if the element has a large interval, compared with
another of similar magnitude but smaller interval.  Perhaps the
element with the largest ratio of magnitude to interval is chosen,
so as to minimize the intervals of the reduced elements?

Anyhow, is there a standard strategy for making these kinds of
choices?  How are error bounds computed in light of these choices?
Is it even a factor?  Does one simply compute as one computes, and
take the final answer as gospel and then tweak the algorithm to
reduce the intervals of the results as much as possible?

			Robert Herndon
-- 
Robert Herndon		    --	not speaking officially for Cray Computer.
Cray Computer Corporation	   --|--		719/540-4240
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