Accuracy of Inputs

[Bill Walster - Staff OACIS]

James Demmel: "No system can read the user's mind as to the accuracy of
the numbers she or her program supplies as input to system routines." 

One of my primary points is that this is an unacceptable condition. We
must devise methods to communicate to systems how accurate inputs are.
This can be done very simply by adopting a convention such as adding or
subtracting one from the last digit input in a given number, thereby
automatically defining an interval. For example .2345 would be
interpreted by the system as [.2344, .2346]. I made such a
recommendation in a paper "Philosophy and Practicalities of Interval
Arithmetic", in "Reliability in Computing" edited by R. E. Moore,
Academic Press, 1988. Once the accuracy of inputs is made explicit, the
need for interval arithmetic becomes even more acute.

James Demmel: "Finally, a comment on interval arithmetic. In the rare
case that the input to an interval subroutine A is exact"

It is my experience as well that exact inputs are rare events. We are in
complete agreement that if exact inputs are to be propagated through an
algorithm, then arbitrarily precise interval arithmetic or exact
rational arithmetic is required. Inexact inputs require only sufficient
accuracy to compute reasonably sharp bounds on the solution set.