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Re: Catastrophic Cancellation
From: |
Sergei Steshenko |
Subject: |
Re: Catastrophic Cancellation |
Date: |
Thu, 3 Jul 2008 23:15:14 -0700 (PDT) |
Applications From Scratch: http://appsfromscratch.berlios.de/
--- On Thu, 7/3/08, Rob Mahurin <address@hidden> wrote:
> From: Rob Mahurin <address@hidden>
> Subject: Re: Catastrophic Cancellation
> To: address@hidden
> Date: Thursday, July 3, 2008, 3:24 PM
> 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
>
> _______________________________________________
> Help-octave mailing list
> address@hidden
> https://www.cae.wisc.edu/mailman/listinfo/help-octave
Thanks for the clarifications.
Perhaps 'octave' documentation should contain links to web pages explaining
the basics/pitfalls of computer arithmetic.
Luckily (?) for me I was first taught numerical methods of computation and
only after that programming - probably it's not the case anymore in modern
world.
Regards,
Sergei.
Re: Catastrophic Cancellation, Francesco Potorti`, 2008/07/03