[Maxima] Maxima Digest, Vol 9, Issue 38
keith.weinman at dlr.de
Fri Apr 13 09:12:20 CDT 2007
Since finite precision numerics are inherent in any computer
representation of a decimal number I think that there are some issues
that are required to be understood by a user. To this end perhaps there
should be a small section in the user guide files dedicated to this
topic (following suggestion of R.Fateman - apologies if my memory is
faulty). Since I have to do something like this for the code I work on,
I will be happy to give a latex file which others can then modify if
they feels so inclined.
Maybe some simple addiitons that can help when people do floating point
comparisons such as (a == b) are by rewriting them as
if (fabs(a-b) < epsilon) ? true : false;
where epsilon is machine epsilon.
This expression is more meaningful in the world of finite precision
numerics. Then of course there are additional steps, such as
reformulation of algorithms to avoid catestrophic cancellation. This
may become more important if MAXIMA really is to be used as a numerical
analysis package as well, however most commercial numerical packages
probably dont worry about these issues too deeply because of run time
costs if all possible sources of fp error are caught.
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