applicability of interval arithmetic

[Bill Walster - Staff OACIS]

David Hough cites an example due to Kahan in which the growth of a naive
interval algorithm experienced exponential growth. Presumably,
reformulating the problem will permit interval bounds on the axes of the
solution ellipsoid to be computed sharply. Is it not the case that the
naive algorithm if implemented in real arithmetic would experience the
same kind of exponential error growth? But, without interval arithmetic,
the naive user might not be alerted to the fact that errors have grown
exponentially. Without this warning, he may not be motivated to search
for a more elegant solution. This kind of scenario is a prime example of
one of the functions of interval arithmetic.