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Re: Catastrophic Cancellation
From: |
Rob Mahurin |
Subject: |
Re: Catastrophic Cancellation |
Date: |
Thu, 3 Jul 2008 18:24:11 -0400 |
On Jul 3, 2008, at 8:50 AM, Sergei Steshenko wrote:
octave:1> (0.3 - 0.2 - 0.1)/1e-16
ans = -0.27756
- I do not understand what you wanted to say by your reply.
I.e. I do not understand what/where the problem is.
There have been a few questions on this list in the past couple weeks
phrased as "how can I get more precision from Octave," but actually
problems of floating-point truncation in numerical analysis. One was
a question about a p-value like 1 - (1e-30). One was perhaps an
arbitrary precision question? This seemed to prompt AK to post his
example of the difference between the three expressions
(1-cos(x)) ./ x.^2;
1./ x.^2 - cos(x) ./ x.^2; and
(.5 - x.^2 / 24)
as computed by octave (or anything else) on the interval between 0
and 1e-7. It really is a pretty example of the sorts of things you
see when you hit a truncation error problem. But it's only Octave-
specific in the sense that Octave is the first introduction to
numerical analysis for many people.
Cheers,
Rob
--
Rob Mahurin
Dept. of Physics & Astronomy
University of Tennessee phone: 865 207 2594
Knoxville, TN 37996 email: address@hidden
Re: Catastrophic Cancellation, Francesco Potorti`, 2008/07/03