Re: General pow(xx,yy) function in Motion 10
Dan Zuras Intervals wrote:
On the contrary, the interval returned for pow(xx,yy)
WILL CONTRACT for each contraction of xx & yy.
And no crash will occur on a correctly written program.
It is just that it will not snap to any particular
manifold (positive or negative) until yy becomes a
singleton.
Then there are two possibilities: Either the solution
you seek is contained within the remaining manifold
when the exponent becomes a singleton or it does not.
If it does you will be able to identify it quite
narrowly in xx as well. If it does not then the
singleton is outside the desired solution space.
Dan, Michel,
Thanks for the clarifications.
Theoretically, I agree an infinite number of bisections in the domain will
contract the range to a point. However, the best that can be done in a
machine is to bisect the domain to a tiny interval with the width of exactly
one ULP. If the endpoints of this tiny interval are large negative numbers,
then the interval range will still be very, very large. In this case, the
branch-and-bound algorithm will request the interval domain should be
further bisected in order to contract the interval range. But this is no
longer possible. So how does the user (or the machine) know which manifold
the solution belongs to?
Nate