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Re: strange problem
From: |
Przemek Klosowski |
Subject: |
Re: strange problem |
Date: |
Fri, 28 Nov 2003 13:40:01 -0500 (EST) |
| It is not just representation. This was hust one in a series of 4000
| matrix multiplications in a script. It gave me the problem of a
| impossible answer,a negative distance in a optical system (this is
| possible just not in the system I'm building).
This is a perfect example why interval arithmetic and/or error-propagation
systems are useful.
You have a rounding error on the order of machine double precision LSB
(eps=2.2e-16), on a value of 0.01; this is a relative error of 1 in 45
trillion, i.e. inaccuracy comparable to an error of 8 microns in the
Moon-Earth distance (*)
If your final result is that sensitive to rounding errors, I would really
look carefully at its accuracy.
In an error-calculating system, you'd specify errors together with
your input parameters; the errors will presumably be much larger than the
numerical epsilon. The final result would come with a confidence interval.
You can simulate this by performing your Octave calculation multiple times,
taking your original your input data and modifying them one-at-a-time by
adding and subtracting the error.
(*) How do I know that? Well, there's this great program called 'units'
(comes out of the box with most Linux distributions). 'units -v' gives:
You have: moondist/(0.01/2e-16)
You want: micron
moondist/(0.01/2e-16) = 7.688 micron
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- Re: strange problem, (continued)
Re: strange problem, Laurent Jacques, 2003/11/28
Message not available
strange problem, John W. Eaton, 2003/11/28
RE: strange problem, THOMAS Paul Richard, 2003/11/28
RE: strange problem, THOMAS Paul Richard, 2003/11/28
Re: strange problem, pkienzle, 2003/11/29