Re: midrad representation
Svetoslav Markov schrieb:
Yes, Arnold,
there should be a document "specifying at least one reasonable version
of what is the proposed alternative".
I am thinking over producing such a document, possibly a position paper.
I think that operations can be specified for narrow intervals.
My wish is that the document comprises both midpoint-radius form and
complete IA both in sup-inf and mid-rad form.
I think that such a position paper need not discuss the infsup form
(except where relevant for the sake of comparison).
I shall be happy if somebody else wishes to join me in writing the
document. May be two documents should be compiled: one on
mid-rad form (within "classical interval arithmetic") and another on
complete (Kaucher/directed/modal...) IA.
Due to my limited experience in writing such documents, I shall be
more happy if someone with such an experience takes the leadership
role. May be you, Arnold?
Not me. I am supporting the Vienna Proposal, and don't want to waste
my time of alternatives.
But of course you can take the Vienna Proposal as a template for your
efforts, to see which issues need to be addressed. And you may
post preliminary versions of your position paper to the list and ask
for feedback, as I had done for the Vienna Proposal.
Here are some points that I consider essential for the sake of clarity:
You need to distinguish between nonoptimal centered arithmetic
(a bit cheaper) and optimal noncentered arithmetic (more expensive),
and say which one you want.
You also need to say what happens in finite precision arithmetic,
and when numbers are +-Inf or NaN.
You also need to say how you want the radius to be represented
(if its format is to be different from that of the midpoint, as
you repeatedly suggested).
You also need to give a clear definition of how to evaluate
elementary functions in midrad arithmetic.
Arnold Neumaier