Re: Motion 13 and the empty set
P1788,
> Therefore my question: DOES ANYBODY HAVE AN IMPOTANT APPLICATION WHERE
>> THE EMPTY SET APPEARS AS AN OPERAND IN AN OPERATION OR A COMPARISON?
>
> I would think the most common occurrence of the empty set would be
> in union and intersection (either as an operand or as a result).
> Are we considering union and intersection as operations?
To the extent possible, we should avoid assuming knowledgeable interval programming.
Suppose a student has programmed an approximate Newton's method, and now sees an interval Newton method. Suppose he understands that he should intersect the current interval with the result of the Newton operator, but forgets that he should check that the intersection is non-empty. After all, there was no isEmpty() check in his approximate code. Now he will try to evaluate f(mid(X)) and Jacobian(X) with empty sets X.
OF COURSE that is wrong, but is a scenario in which empty as an operand to ANY operation can arise.
I could accept treating that as an error, but I think it has to be treated.
I am VERY concerned about pitfalls for students and other interval novices. If they believe what we say about computing with guarantees, but they compute wrong answers because of their own errors, they are likely to blame us and never look at intervals again. We should make it as difficult as we can to do dumb things, or at least not set traps for the unwary.
George
Dr. George F. Corliss
Electrical and Computer Engineering
Marquette University
P.O. Box 1881
1515 W. Wisconsin Ave
Milwaukee WI 53201-1881 USA
414-288-6599; GasDay: 288-4400; Fax 288-5579
George.Corliss@xxxxxxxxxxxxx
www.eng.mu.edu/corlissg