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Containment-only Interval Standard



Several times in the past few years I have asked for explicit recognition
of the fact that there are two very different applications of Interval
Arithmetic:

(1)  Intervals as imprecise single values.

(2)  Intervals as bounded (or semibounded) ranges of separate values.

Bill Walster's position deals exclusively with (1) and is meaningless
for (2).   For (1), narrowness is a valid quality issue, but for (2) it
is not.  In the case of (2), the precision of the bounds is a quality
issue, especially near critical points of a function being computed.

(1) provides a dependable extension of plain FP arithmetic, whereas (2)
supports constraint propagation analysis.

(1) can easily accomodate mid-rad representations; for (2) those would
mostly be meaningless, except perhaps for linear functions.

Michel.
---Sent: 2011-08-03 19:06:54 UTC