Re: Up-to date Interval Arithmetic
Dear colleagues
Please recall that about two years ago I proved the following about Rump arithmetic, as I'll call the system described in Siegfried's 2012 paper.
- It is a 1788 flavor.
- Any instance of it, defined by a particular set of "endpoints", is an interval type of the flavor.
I have not had the chance to check rigorously the relation of Rump arithmetic with Unum arithmetic, but what I learned from hearing John Gustafson talk suggests it is a strong one.
Therefore I think we are in a situation of convergence, not divergence, of these various approaches. In particular let's look forward to a 1788-conforming implementation of Rump arithmetic.
Regards
John Pryce
On 24 Mar 2015, at 23:23, Siegfried M. Rump <rump@xxxxxxxxxxxxx> wrote:
> Dear colleagues,
>
> A theoretical foundation of interval arithmetic with infinitely small (large)
> but nonzero (finite) endpoints is given in
>
> S.M. Rump. Interval Arithmetic Over Finitely Many Endpoints. BIT Numerical Mathematics, 52(4):1059–1075, 2012.
>
> The paper is appended. It covers in particular closed, half-open or open intervals,
> as well as to treat special numbers such as pi as exact data.
>
> Best wishes,
> Siegfried
>
>
> Am 25.03.2015, 05:19 Uhr, schrieb Ulrich Kulisch <ulrich.kulisch@xxxxxxx>:
>
> Dear colleagues:
>
> I attach an unpublished paper entitled:
> Up-to-date Interval Arithmetic - From closed intervals to connected sets of real numbers
> which on request recently was sent to the Reliable Computing Group. You may find it interesting.
>
> Best regards
> Ulrich