Re: Comments on Motion 27-A "Decorated Intervals"
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. 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.
So I stand by what I said. The algorithm is right, the theory is wrongly stated.
> 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.
John