Interval enclosure of X**Y for negative x in X

[Arnold Neumaier]

>>It's a question of error detection.   Typical physics codes exploit
x**y (as opposed to x**n) with expressions like z**0.62
where the 0.62 appears to be an empirical constant (or more complicated
expression) and is not intended to
represent some fraction, so any negative argument z would be an error.<<

In an interval context, (-1.4)**0.62 would be empty, and hence produce
an unsuspected infeasibility result in an optimization routine that
hints at the error if the reporting software is reasonable.
And since empty is sticking (usually), one would also recognize it in
other interval calculations. Whether one checks for empty or for NaN
is the same amount of work on the side of the user.

Arnold Neumaier




<PRE>