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

Dear all,

we (me and Prof. Rump) alreday discussed in 2000 that

     set round up
     m=l+0.5*(u-l);r=m-l

is more accurate so that in INTLAB this formula is used.

Shin'ichi
----- Original Message ----- From: "Arnold Neumaier" <Arnold.Neumaier@xxxxxxxxxxxx> 
To: "Siegfried M. Rump" <rump@xxxxxxxxxxxxx>
Cc: "Shin'ichi Oishi" <oishi@xxxxxxxxx>; "Michel Hack" <hack@xxxxxxxxxxxxxx>; "stds-1788" <stds-1788@xxxxxxxxxxxxxxxxx> 
Sent: Friday, February 13, 2009 9:28 PM
Subject: Re: MidRad to/from InfSup (was: the "set paradigm" is harmful)



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


Shin'ichi Oishi proposed

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.


But in Intlab (version 5.2), you use my new proposal, not Oishi's!


Arnold Neumaier