> Date: Sat, 11 Mar 2006 16:32:06 -0500 (EST)
> From: "John Randall" <[EMAIL PROTECTED]>
> Subject: Re: [Jprogramming] More precision nightmares
> To: "Programming forum" <[email protected]>
John Randall's post with the above heading (but which
Yahoo won't let me include the text of here) concluded
with a suggestion that p j should Google "interval arithmetic"
to find out how to get better computational results.
Interval arithmetic looked good for a while, then went out
of favour because intervals tended to extend out of control.
Then the Europeans looked at sophisticated ways to use
interval arithmetic and ended up with fairly general
techniques for which convergence (which could almost
always be found) PROVES that the correct result is
within the intervals of the result. For information on this,
p j should Google "validated numerics".
I get the impression that the field of validated numerics
is largely unknown outside Europe.
Incidentally, both interval arithmetic and its use in
validated numerics depends on directed rounding, which
was persuaded into the IEEE standard but was
typically implemented in hardware very poorly. It seems
there is a revision of that standard under way in which
some of these issues are being raised again.
Neville Holmes
Neville Holmes, P.O.Box 404, Mowbray 7248, Tasmania
Normal e-mail: [EMAIL PROTECTED]
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