Re: MidRad to/from InfSup (was: the "set paradigm" is harmful)

["Siegfried M. Rump" <rump@xxxxxxxxxxxxx>]

On Thu, 12 Feb 2009 12:15:10 -0100, Arnold Neumaier  
<Arnold.Neumaier@xxxxxxxxxxxx> wrote:

> Shin'ichi Oishi schrieb:
> > > what I proposed is
> > set round up
> > m=0.5*(l+u)
> > r=m-l
>
>
> I think the formula that should be in the standard is
>      set round up
>      m=l+0.5*(u-l);r=m-l
>
> In binary arithmetic, or when intermediate results are kept to higher
> precision, the two formulas appear to be equivalent.

Given this last remark, I suggest to use Oishi's proposal at least
for binary arithmetic:
- it uses only 3 rather than 4 operations,
- the midpoint is always inside [l,u], see Higham: ASNA.

Cheers, Siegfried

--
=====================================================
Prof. Dr. Siegfried M. Rump
Institute for Reliable Computing
Hamburg University of Technology
Schwarzenbergstr. 95
21071 Hamburg
Germany
phone  +49 40 42878 3027
fax    +49 40 42878 2489
http://www.ti3.tu-harburg.de

and

Visiting Professor at Waseda University
Faculty of Science and Engineering
Shinjuku Lambdax Bldg. 902
2-4-12 Okubo, Shinjuku-ku
Tokyo 169-0072
Japan
phone/fax in Japan  +81 3 5286 3414