Re: A mid-rad interchange motion...

[Arnold Neumaier <Arnold.Neumaier@xxxxxxxxxxxx>]

Dan Zuras Intervals wrote:
> > From: John Pryce <j.d.pryce@xxxxxxxxxxxx>

> > - Define an interval type to be an inf-sup or mid-rad type depending
> > on its level 3 representation:
> >   An inf-sup interval type is one whose level 3 representation by 
> >   floating-point numbers lets the lower and upper bound of each
> >   nonempty interval of that type be retrieved exactly.
> > and
> >   A mid-rad interval type is one whose level 3 representation by 
> >   floating-point numbers lets the midpoint and radius of each
> >   nonempty [add "bounded" here?] interval of that type be 
> >   retrieved exactly.
> >
> > Letting level 3 drive the definition looks perverse, but it seems
> > to me that's where the essence of the two kinds of type lies. 
>
> 	It looks perverse to me as well.  I think of the
> 	distinction as living at the set of values each
> 	form represents.  Therefore, level 1.
>
> > However, I'm not sure whether a "mid-rad1-rad2" type admits a
> > definition on these lines, because of the extra degree of freedom
> > in describing it by 3 numbers instead of 2.

Actually, one should think of "mid-rad1-rad2" as center+error-interval,
thus it is composed of two objects, a center and an error interval,
possibly of different precisions.