Re: Siegfrieds recent paper
Am Mi 04.01.2012 16:09 schrieb Vincent Lefevre <vincent@xxxxxxxxxx>:
> This is a particular example.
... and constructed, I agree.
> I think that in most of the cases,
> your arithmetic won't bring anything better.
In my arithmetic
A = infsup(0,1000); % [0,1000]
B = exp(A); % [1,inf]
C = 1/B; % [T,1]
D = infsup(0,0); % [0,0]
E = intersect(C,D); % empty
Truely empty, without decoration.
In P1788
A = infsup(0,1000); % [0,1000]
B = exp(A); % [1,inf]
C = 1/B; % [0,1]
D = infsup(0,0); % [0,0]
E = intersect(C,D); % [0,0]
> And you may generate
> unnecessary NaI's, e.g. when one knows from the context that the
> result is well-defined (i.e. when undefinedness in some operations
> comes from the fact that intervals are supersets of the range of
> the real results).
>
If we know from the context that the function is well-defined, I agree.
My concern is what happens if P1788 produces
A = infsup(0,1000); % [0,1000]
B = exp(A); % [1,inf]
C = 1/B; % [0,1]
D = 1/C; % [1,inf] with decoration
and D is used forgetting to check the decoration. The conclusion may be
that an underlying function is well-defined, but it is not. This cannot
happen with my definition.
Cheers,
Siegfried
=====================================================
Prof. Dr. Siegfried M. Rump
Institute for Reliable Computing
Hamburg University of Technology
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and
Visiting professor at Waseda University
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