Re: Remarks on Motion 11
John Pryce wrote:
One remark: I believe that Corollary 1 is false---which should
address the question raised by Nate Hayes' mail. For example, take
A=[0,2]
B=[-1,1]
C=[1,1]
Good point. Thanks for clarifying it. It's the order in which "hull"
and "intersect" are done that makes the difference, I think.
A few comments/observations:
-- The result [1,2] may be obtained without reverse mode by checking if
zero is an element of B and then processing each side of the branch-cut
separately.
-- The same is true if A=[-2,2], i.e., if zero is element of B the
intervals
[-2,-1]=(-oo,-1] \intersect [-2,2] and [1,2]=[1,+oo) \intersect [-2,2]
are obtained without reverse mode operations. In interval Newton, it is
advantageous to process intervals [-2,-1] and [1,2] separately, rather than
their union [-2,2].
Sincerely,
Nate