Re: Sorry, my example in error Re: Tetrits and "stickiness"
Dan Zuras Intervals wrote:
Now that you have me thinking about it what about the
map g(x) = x - 1 on the input set x = [-oo,5]? The
iteration will produce an ever contracting (in the
sense of subset) series of intervals but there is no
fixed point unless you consider -oo to be a element of
our topology.
Actually, come to think of it, g() will never contract
beyond [-oo,-b^p] where b is the base & p is the
precision since at that point we will have
roundUp(-b^p - 1) = -b^p.
I'm very interested to study/know what should be the correct behavior of
branch-and-bound methods on these types of conditions, i.e., unbounded
entpoints. It's what I tried (rather poorly) to ask in my 4/12 post, e.g.,
what is the correct range enclosure and decoration for the sequence of
nested intervals
g((-oo,a1]) \supseteq g((-oo,a2]) \supseteq ...
NOt only for reasons that Dan mentions, but also since in fact the
intersection of the sequence
(-oo,a1] \supseteq (-oo,a2] \supseteq ...
is empty! Am I correct the branch-and-bound method needs to return [empty]
along with some exceptional decoration state in this case? Or is there some
better way to handle it?
Nate