Re: mid-rad, inf-sup, a caution...

[Arnold Neumaier <Arnold.Neumaier@xxxxxxxxxxxx>]

http://en.scientificcommons.org/mariana_kolbergRudnei Cunha wrote:
> Hi,
>
> There are some interesting results on the works by M. Kolberg, D. M. Cláudio
> et al., which show that for interval linear systems, not only one can get
> better enclosures with mid-rad, but also the implementation may be more
> efficient, including with respect to a parallel interval computation. Here
> is such a paper:
>   Improving the Performance of a Verified Linear System Solver Using
> Optimized Libraries and Parallel Computation (2008)
>
> http://drops.dagstuhl.de/opus/volltexte/2008/1438/

This is just Rump's trick (cited on p.3) for the evaluation of the
Krawczyk operator.

Note that Rump's trick does not use midrad intervals as datatypes,
but a midpoint matrix and a radius matrix, stored and manipulated
as real matrices, and created and used only in an intermediate
calculation of the algorithm.

The algorithm would not benefit the slightest from the availability
of a midrad interval arithmetic.


Arnold Neumaier