Re: Comments on Motion 27-A "Decorated Intervals"
John Pryce wrote:
Nate
On 16 Jul 2011, at 16:21, Nate Hayes wrote:
What's wrong is Theorem 3. If that is all one can trust to be true, it
seems to me the current draft can't handle Nate's branch and bound
application. Suppose one computes ndf. According to Theorem 3, con might
be true, or even saf!
???
If one computes ndf *by Definition 8*..., then f
is certainly not defined on xx.
What you say is true, we all agree on that.
Ok. Good.
I disagree with the omitted bit
(which is what Theorem 3 says)
Theorem 3 is imprecisely stated, but the only meaning I can attribute to
it is
(Computed decoration of f over xx) <= (true decoration of f over xx).
IF THAT IS ALL ONE CAN TRUST TO BE TRUE, one cannot justify your B&B
method.
Ok. Thanks for the clarification.
However, in my reading of the text, it simply says (in so many words):
"By Definition 8, the worst decoration in the DET is propagated to the
end."
That's all the B&B method requires, so in this interpretation Theorem 3 is
valid.
So I stand by what I said. The algorithm is right,
Yes.
the theory is wrongly stated.
As noted, I don't see it gives the meaning you ascribe to it above.
In any case, I wouldn't object wordsmithing it for better clarity, so it
doesn't have double meanings depending on one's interpretation of the text.
I think you missed the point Vincent was making: sometimes in
pathological
cases the decoration con might be returned when f is actually undefined
over
xx. But that's not a failure (even FTDIA says so).
That's a different point, which I appreciate and agree with. My recent
silly example of evaluating
f(x) = sqrt(-1-x*x)
at xx = [-2,2] is another example of this.
Yes.
Nate