2010/5/4 Vincent Lefevre
<vincent@xxxxxxxxxx>
On 2010-05-02 03:54:20 -0700, Dan Zuras Intervals wrote:
> The 'dubious' nature of my concerns surround the
> problem that mid-rad intervals represent a quite
> different subset of the Real intervals than do the
> inf-sup forms. I believe that it will require us
> to burden mid-rad forms further to represent these
> intervals (like [1e-100,1e+100] & [3,+oo]) somehow.
> Is it sufficient to represent them as say,
> (5e+99,0,1e+100) & (something+3,-something,+oo)?
I think that if the interval is large enough, one can still choose
mid = 0. Then the representation is equivalent to inf-sup, isn't it?
My understanding of the form (mid, del1, del2) that represents [mid-del1, mid+del2] was that both del1 and del2 are always considered as zero or positive numbers (the distance of the radius). However, taking mid=0 for large intervals leads to negative or positive delimiters as in:
[-1e+10, 2e+20] = (0, 1e+10, 2e+20)
[+1e+10, 2e+20] = (0,-1e+10, 2e+20)
[-1e+10, -2e+20] = (0, 1e+10, -2e+20)
Vincent's proposal solves the issue of representation for large intervals. However, can the colleagues who use mid-rad representations in their work comment on whether they depend on the fact that rad is always non-negative? If yes, what is the impact of having two delimiters (not just one) and with both being either positive or negative?
--
Hossam A. H. Fahmy
Assistant Professor
Electronics and Communications Engineering Department
Cairo University
Egypt