From: skaller <skaller@ozemail.com.au>
To: Ocaml Mailing List <caml-list@inria.fr>
Subject: Re: [Caml-list] float type with better precision than the default
Date: 06 Dec 2003 14:42:50 +1100 [thread overview]
Message-ID: <1070682167.6259.31.camel@pelican> (raw)
In-Reply-To: <Pine.LNX.4.44.0312052104040.5009-100000@localhost.localdomain>
On Sat, 2003-12-06 at 14:18, Brian Hurt wrote:
> 30 decimal digits is enough accuracy to measure the
> distance between here and the Andromeda Galaxy in microns. Why does he
> need such a ridiculous amount of precision?
Standard eigen problem sometimes needs ridiculous precision:
the scalar product of two vectors:
sigma (i=1,n) (v1_i * v2_i)
sometimes involves cancellation of large values.
To see why there is a problem here, consider:
1.000001e20 - 1e20 -
(1.000001e-20 - 1e-20)
and you can see you need around 50 digits precision, just to get
an answer with 1 digit of precision.
The eigen problem with large numbers of dimensions
arises in, for example, quantum chemistry.
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next prev parent reply other threads:[~2003-12-06 4:42 UTC|newest]
Thread overview: 7+ messages / expand[flat|nested] mbox.gz Atom feed top
2003-12-06 0:44 romildo
2003-12-06 3:18 ` Brian Hurt
2003-12-06 3:42 ` skaller [this message]
2003-12-06 11:54 ` Remi Vanicat
2003-12-08 10:11 ` Jean-Christophe Filliatre
2003-12-08 11:29 ` Jean-Christophe Filliatre
2003-12-08 11:57 ` romildo
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